STATISTICAL ANALYSIS OF RADIATION DOSE DERIVED FROM INGESTION OF FOODS By WARD L. DOUGHERTY A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2001 Copyright 2001 by Ward L. Dougherty Dedicated to Gwen, Justin and Michelle The Best Family in the World! ACKNOWLEDGMENTS I would first and foremost like to thank my wife, Gwendolyn, whose constant encouragement and support provided the impetus as well as the confidence to finish when it seemed a daunting task. My best daughter in the world, Michelle, and best son in the world, Justin, gave me the time and the "I Love You, Dad" at the times I needed them the most. I see them growing more each day, and this task of writing a dissertation seems insignificant to my task in parenting. You, as my family, make me more proud than anything else that I have done in this life. I would like to offer a special thanks to Dr. W. Emmett Bolch. He provided me support at the times when I needed it the most and encouragement and support when it was hard to find. My professors~Dr. Anghaie, Dr. Wesley Bolch, Dr. Dalton, Dr. Properzio, and Dr. Lindner—have been invaluable in providing not only their time and assistance but also their support throughout this endeavor. My friends-Travis Knight, Gary Chen, Paula Johnson, Katherine Wilson, and Steve Boddeker— were a great help in providing suggestions as well as listening and offering insight to help me complete this work. Much of this work would not have been possible without the assistance of Jerome Guidry, Brian Birky, and Cindy Hewitt. Their assistance and help have been invaluable both in the content and the background for this work. IV TABLE OF CONTENTS page ACKNOWLEDGMENTS iv ABSTRACT vii CHAPTERS 1 INTRODUCTION 1 Radioactive Dose to the Public 5 Hypothesis 5 Goals and Objectives 6 2 LITERATURE SEARCH 7 Introduction 7 Dietary Intake Data 7 Concentration of Radionuclides in Food 10 Dose Conversion Factors 1 1 Statistical Considerations 12 3 DIET MODEL 13 Introduction 13 Initial Model 14 NRC Nuclear Regulatory Guide 1.109 14 RESRAD 17 Environmental Protection Agency 18 United States Department of Agriculture 19 Conclusion 21 4 EXPERIMENTATION 25 Introduction 25 Initial Store Samples 25 Grocery Store Analysis 32 Rice Experimental Analysis 37 Histogram Analysis 43 Conclusion and Recommendations for Future Research 47 5 DOSE CONVERSION FACTORS 50 Introduction 50 Literature Search 50 Discussion 51 Conclusion and Recommendations 52 6 COMMITTED EFFECTIVE DOSE EQUIVALENT 54 Introduction 54 Literature Search 55 Method 55 Analysis of 1990 FIPR Dose Diet 57 Grocery Store Data Analysis 63 Overall Analysis 67 Conclusions 72 7 CONCLUSIONS AND RECOMMENDATIONS 75 APPENDICES A DATA SHEETS 80 B CRYSTAL BALL OUTPUT DATA '. 101 REFERENCES 206 BIOGRAPHICAL SKETCH 209 VI Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy STATISTICAL ANALYSIS OF RADIATION DOSE DERIVED FROM INGESTION OF FOODS By Ward L. Dougherty May 2001 Chairman: Emmett Bolch Major Department: Environmental Engineering Sciences This analysis undertook the task of designing and implementing a methodology to determine an individual's probabilistic radiation dose from ingestion of foods utilizing Crystal Ball. A dietary intake model was determined by comparing previous existing models. Two principal radionuclides were considered~Lead-210 (Pb-210) and Radium 226 (Ra-226). Samples from three different local grocery stores-Publix, Winn Dixie, and Albertsons—were counted on a gamma spectroscopy system with a GeLi detector. The same food samples were considered as those in the original FIPR database. A statistical analysis, utilizing the Crystal Ball program, was performed on the data to assess the most accurate distribution to use for these data. This allowed a determination of a radiation dose to an individual based on the above information collected. Based on the analyses performed, radiation dose for grocery store samples was lower for Radium-226 than FIPR debris analyses, 2.7 vs. 5.91 mrem/yr. Lead-210 had a Vll higher dose in the grocery store sample than the FIPR debris analyses, 21.4 vs. 518 mrem/yr. The output radiation dose was higher for all evaluations when an accurate estimation of distributions for each value was considered. Radium-226 radiation dose for FIPR and grocery rose to 9.56 and 4.38 mrem/yr. Radiation dose from ingestion of Pb- 210 rose to 34.7 and 854 mrem/yr for FIPR and grocery data, respectively. Lead-210 was higher than initial doses for many reasons: Different peak examined, lower edge of detection limit, and minimum detectable concentration was considered. FIPR did not utilize grocery samples as a control because they calculated radiation dose that appeared unreasonably high. Consideration of distributions with the initial values allowed reevaluation of radiation does and showed a significant difference to original deterministic values. This work shows the value and importance of considering distributions to ensure that a person's radiation dose is accurately calculated. Probabilistic dose methodology was proved to be a more accurate and realistic method of radiation dose determination. This type of methodology provides a visual presentation of dose distribution that can be a vital aid in risk methodology. Vlll CHAPTER 1 INTRODUCTION The purpose of this study was to design and implement a methodology utilizing the Crystal Ball* program to determine a statistical value, a number, and associated fluctuation of an individual's radiation dose based on foods bought from local stores in Gainesville, Florida, and to provide comparison through analysis to a similar previous study. The most straightforward approach to an individual's radiation dose determination has been to use a deterministic approach. The calculation stated below will provide a committed effective dose equivalent (CEDE) based on ingestion (intake) of a specific radionuclide, a certain concentration in the food and a dose conversion factor (DCF). Intake * Concentration * DCF = CEDE (Equation 1-1) where Intake = individual dietary intake (g/day or g/yr) Concentration = amount of radionuclide in for (pCi/g or pCi/kg) DCF = dose conversion factor—term to convert activity in foods ingested to dose (mrem/pCi). Crystal Ball is a statistical analyses program written by Decisioneering as an addition to Microsoft Excel. This provides Monte Carlo sampling of input parameter distribution and trials to determine an output distribution. 1 CEDE is a dose quantity that describes the long-term dose to an individual from an intake of radioactive material (Shleien, Slaback, & Birky, 1998, pp. 3-5). Depending on what type of dose the individual was trying to calculate, each variable in the calculation had essentially one, and only one, value determined and set down in the guidelines by various agencies. The guidelines were put into recommendations, and these were subsequently, though much later, written into regulatory guidelines. The advent of better computational methods for radiation dose determination due to better computer hardware and software and increased amounts of experimental data is now leading to more accurate determination of the described dose utilizing a probabilistic approach. The method of a probabilistic approach versus deterministic approach utilizes the information that the variables are each described by a statistical distribution. These statistical distributions are defined by a mean and its associated fluctuations. Figure 1-1 illustrates the methodology and the concept behind this approach. This method provides a more accurate description of the actual range that each variable might have and the probability assigned to it. ». T ». ! dt ] * * tatfM i; i & 1 fc \ P>', ; J Intake Distribution Concentration Distribution DCF Distribution CEDE Dose Distribution Figure 1-1. Probabilistic Method of Dose Calculation The Health Physics Society has stated in their most recent position papers that risk assessment must be considered in the context of uncertainties in the estimates (Burk, 2000, p. 232). This statement is in light of the fact that more people and organizations are approaching risk-based policy. This approach allows determination of a final answer, in this case dose, that also has a distribution. This type of an answer, final dose described by a distribution, provides a more accurate answer by taking into account the distributions of the variables with their associated errors and promulgating them through the equation to come to a final solution. This document is set up as individual chapters connected by the overall introduction and conclusion. Each chapter has its own introduction and conclusion. Additionally, each chapter describes the previous and following chapters to provide a more unified whole to the reader. The chapters in this document and a brief description of each are organized as follows: Chapter 1 (Introduction). This chapter provides an overview of the project of both its scope and breadth. The types of approaches to radiation dose evaluation are discussed, both past and present. A brief overview of the different sections of the chapter is discussed. Chapter 2 (Literature Search). The applicable literature is cited in this chapter. The various studies that have been performed that are specific to the radionuclides, methodology, statistics, and research in this area are reviewed in this chapter. Additional sources are reviewed to determine current work in the area of food radioactivity analysis and diet models utilized to determine dose to an individual. Chapter 3 (Diet Model). The literary references for the individual diet is provided in this chapter. The methodology for determination of the amended diet is discussed in this chapter. The diet is described for an individual in this portion of the paper. A determination of an individual's intake is made in this chapter as well as the rationale behind the decision. Chapter 4 (Experimentation). Description of the samples bought, prepared, and counted from three different local stores is considered in this chapter. Concentration data for various foods is determined from the experimental data collected. The distribution of the concentration of radionuclides in food is also undertaken and resolved in this chapter with the analysis of an additional set of samples. Chapter 5 (Dose Conversion Factors). Explanation of the Environmental Protection Agency's Dose Conversion Factors (DCFs) is provided. The discussion of the various dose conversion factors is considered, and assignment is made to a statistical distribution to the dose conversion factor variable. Chapter 6 (Committed Effective Dose Equivalent-CEDE) . Analysis of the previous chapters with regard to the calculation of the CEDE is considered utilizing Crystal Ball's statistical analysis tools to configure the variables and determine the output. The various methodologies and analyses on both the original 1990 data and the newly measured grocery store data are presented to determine the final dose and the final dose distributions that accompany these data. Chapter 7 (Results, Conclusions, and Recommendations). The analysis of the final dose determinations and the program to achieve them are presented. Recommendations for future work are presented, and conclusions based on the output from the above chapters are provided. Radiation Dose to the Public An individual is expected to get an average annual dose of 360 mrem (Shleien 1998). Geographic and other factors can change this value from 75 to 5000 mrem. Individuals are constantly exposed to radiation of all types: cosmic, terrestrial, natural internal. Without sunlight life itself would be impossible, but radiation has a bad connotation to the public. People fear the word and the associated images that it conjures up. The public thinks of Three Mile Island and Chernyobl when the issue is discussed, but radiation is all around us and is a vital and important part of our world. The plants are the focus of this paper. This dissertation and chapter seek to determine through theory and experimentation what level of radioactivity is found in our food and provide a statistical analysis for an improved completeness of description. Hypothesis The hypothesis of this dissertation is that the ingestion of radioactivity found in of foods bought from local stores should be measured and analyzed to determine its significance. This value that is experimentally measured from foods should have a statistical value that can be described by a distribution. The final dose that is determined from these measured values additionally should have a statistical value with a distribution. Goals and Objectives The following provides a list of goals and objectives for this dissertation: 1 . Perform a literature search on radioactivity of foods bought in local stores in Gainesville, Florida, as well as previous studies performed on Florida foods or the associated radionuclides. 2. Determine a dietary intake of foods based on previous studies. 3. Measure foods bought from three different local stores and determine radioactivity of lead-210 and radium-226 in these samples. 4. Measure one set of samples to determine distribution to be associated with concentration of radionuclides in food. 5. Determine the distribution to utilize for the EPA's Dose Conversion Factor. 6. Perform Crystal Ball analysis to determine the final dose, in distribution form, to the individual from the original FIPR study data and from the experimentally measured grocery store data. 7. Analyze the results to provide a comparison to the total dose. 8. Compare deterministic and probabilistic methodology of dose calculation. CHAPTER 2 LITERATURE SEARCH Introduction This dissertation covers several fields of study; therefore, a literature search needs to be performed to find the relevant references in each of these areas. The areas of search that are involved in this dissertation are dietary intake, food concentration, radionuclide, dose conversion factors, committed effective dose equivalent, and statistical distributions. This literature search examines the various literature sources that were utilized for each of these categories. Dietary Intake Data The dietary intake of an individual is quite often information that is specific to the individual. The dietary intake varies by person due to individuality of the person as well as local customs and availability of food. In an effort to determine dietary intake of an individual in Florida, the first source that was researched included previous studies performed in Florida. A study of radioactivity in Florida foods and the diet of Floridians necessarily begins with an assessment of study in the field, both past and present. Some of the most recent work in Florida that has examined radioactivity in foods in Florida was performed by the Florida Institute of Phosphate Research (FIPR) (Guidry, Roessler, Bolch, McClave, Hewitt, & Abel, 1990). This organization was created by the Florida Legislature in 1978 to conduct supportive research to the development of the state's phosphate resources. This organization has done studies in this field due to its interest in the environmental aspect of phosphate mining. There are three sources that provided information both for the dietary model and the initial concentration of radionuclides in food grown on phosphate and related lands. The first document is the 1986 FIPR report that provided the initial analysis of radium- 226, lead-210, and polonium-210 in foods grown on phosphate lands (Guidry, Bolch, Roessler, McClave, & Moon, 1986). The initial diet model that describes dietary intake was first presented in this document. The method of analysis and the dose evaluation were described in this book. Simplified analysis of radionuclide concentration in foods was performed to determine dose to an individual. Three individuals were considered: control, local, and maximum. A control individual was a reference individual who consumes "sampled" foods not from mining-related lands. A local individual consumed 10 percent of his "sampled" foods from phosphate lands and 90 percent from control lands. A maximum individual consumed 100 percent of "sampled" foods in his diet from phosphate (clay) lands. This individual reflects worst case scenario (Guidry et al., 1990, pp. 118-119). The next two documents were associated with this initial document. Brian Birky's master's thesis referred to the previous document and used the same methodology, diet, and radionuclides to determine dose attributable to technological enhancement of this phosphate reclaimed land (Birky, 1990). This document detailed the previous methods and studies that were utilized to prepare, enclose, and measure the experimental samples. This thesis discussed the methodology utilized to calculate the dose to an individual directly from the dietary intake spreadsheet. This thesis was much more descriptive in the details of diet and dose calculation than the initial paper. The 1990 FIPR paper was a continuing study based on the recommendations of the 1986 FIPR paper mentioned above (Guidry et al., 1990). This paper utilized the same basic dietary intake model of the initial study. Some of the same radionuclides were considered. This document focused primarily on three radionuclides and five land types. Three types of individuals were considered in this paper also: local, control, and maximum. The basic dietary model, with few revisions, was presented in this paper. This paper analyzed the differences in the data as well as performing regression analysis on the collected data. This paper had more data points added and more analysis performed that detailed the soil-to-plant transfer model and refined the dietary intake model. FIPR has continued to improve its database with more samples since this report, and the extended database will be available in a publication in the near future. The current research and work also has continued to smooth the statistical data. An important point was brought about by direct discussion with Dr. Birky: sampled versus nonsampled diets (B. Birky, personal communication, March 13, 2001). A vital consideration in any analysis is the thought given to what foods were and were not sampled and how to consider them in the final dose determination. These papers and the subsequent meeting provided invaluable insight into this particular point. These papers primarily discuss the various analyses performed on foods grown on Florida lands in general and phosphate lands in Florida in particular. These were the most useful and pertinent with regard to this analysis. 10 Concentration of Radionuclides in Food The concentration of radionuclides in food has been studied in several areas and contexts. The previous three papers discussed this very subject and determined the concentration of several radionuclides in various foods grown on phosphate-related lands. A study funded by FIPR and performed by the Audubon Society studied the concentration of radium-226 in alligators, armadillos, and soft and hard shell turtles (Pritchard & Bloodwell, 1986). These data relate that the hazard from eating these mammals on mine-impacted lands is unclear. Dietary intake of lead-210 has been discussed in several articles. Linsalata (1994) discusses human exposures along plant and animal pathways to thorium, uranium, radium, lead, and polonium. The exposure pathways were considered, and the author states that much more work needs to be done in assessing the transfer of lead- 210 and polonium-210 in the human food chain. Morse and Welford (1971) discusses the dietary intake of lead-210 in the diet of New York city residents with a result of 1.2 pCi lead-210 per day. This food diet only included 19 food items. An interesting note is the fact that the concentration of lead-210 was calculated as 0.70 pCi lead-210/kg food. An analysis was performed on radionuclide contact in Hong Kong food. Yu and Mao (1999) gives an excellent description of the types of gamma spectroscopy system used. The diet model and the results were detailed in tabular form with seven radionuclides under examination. Potassium-40 was found in all solid food and drink 11 samples. Lead-210 was measured as being greater than half the contribution to the dose from natural radioactivity. Carvalho (1995) analyzed the Portuguese population for intake of polonium-210 and lead-210. The author primarily examined these two radionuclides and their ingestion rates for the population. This paper supports the postulation of a different diet model for a different population. The point is also made in this paper that cooking the various food prior to eating is not taken into account. Dose Conversion Factors The data for the dose conversion factor (DCF) came from four sources. The first source was Federal Regulatory Guide No. 1 1 (EPA, 1988, pp. 155-179). This document provides the methodology used to calculate the DCFs for inhalation, submersion and ingestion. The tables of the various DCF data for various radionuclides is included in this manual. The next two articles, International Council on Radiation Protection (ICRP) 68 (ICRP, 1994) and 72 (ICRP, 1996), provide age-dependent DCFs for workers and members of the public from intake of radionuclides. Although they were examined for the purposes of this report, the new DCFs were not utilized for the purposes of consistency. The fourth reference for these data was a solution manual that calculated a dose conversion factor for strontium-90 (Turner, Bogard, Hunt, & Rhea, 1988). This was utilized as a reference to describe the method to obtain a dose per unit intake factor from the initial data. 12 Statistical Considerations Statistics play a major role in the analyses of this study. Information to utilize Crystal Ball comes from the manual provided with the program (Decisioneering, 1996). The manual provides the instruction to utilize the program as well as examples to familiarize the novice with the operation of the various tools built into the software. These sources provided the nucleus of the reference material researched to obtain the necessary data for the background to perform this research and analysis. The following chapter discusses the diet model and how it was determined. The next chapter discusses the dose conversion factor to determine which dose conversion factor to use and what distribution to assign to this value for an accurate estimate of dose distribution. CHAPTER 3 DIET MODEL Introduction This chapter is a literature search and subsequent analysis of various diet models currently utilized by regulatory agencies and other organizations. The object of this portion of the work is to determine the most accurate diet model for calculating radiation dose to individuals in Florida from their dietary intake. The choice of a proper diet model is vital to determine dose to an individual from ingestion. Diet model is not as accurate a term as dietary intake model. This distinction may seem small, but it is significant. A diet model refers to the assumed or predicted intake of certain sources of food to individuals. Conversely, a dietary intake model utilizes surveys of the public to ascertain actual food intake. The goal of this chapter is to ascertain, using major and well-established sources, the most accurate and comprehensive source for the dietary intake model for use with our dose evaluation model. Numerous sources were researched to obtain this goal. The major sources researched were the Pennington Model, Nuclear Regulatory Commission, the United States Department of Agriculture CHFSII 1976-1978 Study, the 1994-1996 NFCS study, RESRAD, and the Environmental Protection Agency. All of these were studied to determine the most suitable diet model for use with a program to determine dose to the individual. 13 14 Several factors are considered in an effort to determine the right dietary intake source for our program and dose determination program. The factors that will be considered to decide on the right source for the final dietary intake model will be the following: the date of the publication, the sources of the publication, the comprehensive quality of the data, and the compatibility with the previous FIPR model. Initial Model The diet model used to calculate radiation dose in the 1986 and 1990 FIPR studies was the 1983 Pennington dietary intake model (Pennington, 1983). The Pennington diet model was derived from the Food and Drug Administration's Total Diet Study. The most recent revision of this study was based on data from the 1987-88 National Food Consumption Survey (Pennington, 1992). This information was discussed in the 1990 FIPR study dealing with radioactivity of foods grown on phosphate lands (Guidry et al., 1990). The dietary intake model used only the adult male category and regrouped the 201 items in the Pennington diet intake model. Table 3-1 shows the data from that paper. As can be seen from this table, there are 17 major categories and 43 subcategories. It detailed intake in grams per day. The sources that are being studied need to be examined to determine unit compatibility and possibility of improvement over this initial model. NRC Nuclear Regulatory Guide 1.109 The first alternate source examined was the Nuclear Regulatory Commission. The mission of the U.S. Nuclear Regulatory Commission (NRC) is to ensure adequate protection of the public health and safety, the common defense and security, and the Table 3-1: Diet Food Items from Pennington Diet (Guidry et al., 1990) 15 Source Intake Item (g/day) DAIRY Milk 280.99 Cheese 22.41 MEAT Beef 129.27 Pork 39.54 Other 69 FISH 20.06 EGGS 30.95 CEREAL FOOD Corn Grain 5.18 Grain 4.55 Cereals/Bread 174.7 CAULIFLOWER/BROCCOLI Cauliflower 0.71 Broccoli 2.8 LEAFY/COLE VEGETABLE Cabbage 7.04 Collard Greens 0.45 Lettuce 23.38 Mustard Greens 0.45 Spinach 3.28 Turnip Greens 0.45 Other 0.76 Celery 0.62 LEGUMES Green Peas 7.29 Other Beans 25.71 Nuts 4.94 Other 11.28 Source Intake Item (g/day) SEEDS/GRAINS B lackeyed Peas 5.61 Rice 22.94 Yellow Corn 14.41 TUBERS/ROOTS Carrots 2.92 Onion 4.19 Radish 0.32 Turnip 0.42 Potatoes 85.22 Other 1.1 GARDEN FRUIT Cucumbers 2.62 Greens Beans 8.8 Green Peppers 1.99 Strawberries 1.23 Tomato 25.18 Watermelon 3.44 Yellow Squash/Zucchini 1.26 Other 6.55 TREE FRUIT Citrus Orange 85.26 Grapefruit 7.78 Lemon 10.71 Other 60.36 SOUPS 36.82 CONDIMENTS 54.12 DESSERTS 78.3 BEVERAGE 1172.44 WATER 512 TOTAL 3071.8 16 environment in the use of nuclear materials in the United States (NRC, 2000). This board and its associated bureaucracy accomplish this mission by presiding over the various aspects of reactor operation, siting, and licensing. Numerous programs and regulations are employed to determine the safety and feasibility of siting and operating a plant. NRC Regulatory Guide 1.109, Calculation of Annual Doses to Man from Routine Releases of Reactor Effluents for the Purpose of Evaluating Compliance with 10 CFR Part 50, Appendix I, employs a dietary intake model to determine dose to an individual from ingestion of radionuclides (NRC, 1977). Tables 3-2 and 3-3 list the consumption of various foods such as fruits, vegetables, meat, and milk. This information is listed for various groups of people: child, teen, and adult. Additionally, each table details the intake for the average individual and the maximum individual. The data in these tables come from ICRP Pub # 23 from 1975 (NRC, 1977) and AER USDA report of 1974 (NRC, 1977). There are only six categories displayed in Table 3-2 and seven categories in Table 3-3. The data are limited when compared to the Pennington dietary intake model. The units are compatible when converted. Table 3-2: NRC NRG 1.109 Average Individual Intake (NRC, 1977) Source Child Teenage Adult Fruits, Veg and Grains (kg/yr) 200 240 190 Milk (L/yr) 170 200 110 Meat and Poultry (kg/yr) 37 59 95 Fish (kg/yr) 2.2 5.2 6.9 Seafood (kg/yr) 0.33 0.75 1 Drinking Water (L/yr) 260 260 360 17 Table 3-3: NRC NRG 1.109 Maximum Individual Intake (NRC, 1977) Source Child Teenage Adult Fruits, Veg and Grains (kg/yr) 520 630 520 Leafy Veg (kg/yr) 26 42 64 Milk (L/yr) 330 400 310 Meat and Poultry (kg/yr) 41 65 110 Fish (kg/yr) 6.9 16 21 Seafood (kg/yr) 1.7 3.8 5 Other Seafood (kg/yr) 1.7 3.8 5 Drinking Water (L/yr) 510 510 730 RESRAD RESRAD was researched next. This program was designed by the Environmental Assessment Division of Argonne National laboratories. It was approved by the Department of Energy for evaluation of radioactively contaminated sites (ANL, 1989). This code has undergone several benchmarking analyses. The first release of the code was in 1989. It allows either user input of numerous variables or default variables. Table 3-4 shows these data in tabular form. As can be seen from this table, there are only five food groups in this diet. Table 3-4: RESRAD Dietary Intake Parameters (ANL, 1989) Source Default Units Min Max Fish 5.4 kg/yr 1000 Other seafood 0.9 kg/yr 100 Fruit, Veg and Grain 160 kg/yr 1000 Leafy Vegetable 14 kg/yr 100 Meat and Poultry 63 kg/yr 300 18 There are various sources for this chapter. The seafood data come from the EPA recommendation of two reports performed in 1981 and 1982. The data for the fruit, vegetable, and grain come from the EPA 1990 paper which was derived from two earlier documents: Foods Commonly Eaten by Individuals: Amount Per Day and Per Eating Occasion and Food Consumption: Households in the United States, Seasons and Year 1977-1978. Additionally, since the 1990 document did not address grain consumption, these data were taken from the NuReg 1 . 1 09 discussed above. For the leafy vegetable consumption rate, the code refers back to NuReg 1 . 1 09 and the average individual. The meat and poultry consumption rate is also determined from NuReg 1.109 and the EPA's 1990 paper with comparison to another paper by Gilbert et al. from 1983. This database, like the NRC model, has a limited number of data points. The units are compatible, but due to the data point limitation, it is not considered as feasible for our diet intake model (ANL, 1989). Environmental Protection Agency The Environmental Protection Agency (EPA) has numerous documents, as is evidenced by the above discussion of RESRAD information sources. The most applicable of them is The Exposure Factors Handbook (EPA, 1997). This was first published in 1989 with its update published in 1997. This paper has a wealth of information about food consumption by area, age, sex, and various foods; however, this information is far too voluminous to include in this chapter. The key study utilized to perform this analysis was the EPA analysis of 1989-1991 USD A CSFII study (USD A, 1996). It should be noted here that this analysis in the exposure factor handbook also 19 included mean and standard errors that might be useful in statistical analyses performed as an extension of this work by future researchers. The EPA's Federal Guidance Report # 13 : Cancer Risk Coefficients for Environmental Exposure to Radionuclides (EPA, 1995) was also researched but was not seriously considered due to the fact that the intake considered is not broken down by food groups, and the units are in kcal/day, units that are not compatible with our comparison. The limited number of data points also make it incompatible with the previous study. United States Department of Agriculture The United States Department of Agriculture (USDA) conducts several food consumption surveys at regular intervals. One of these was mentioned as a reference in the EPA Exposure Factors Handbook (EPA, 1997). Numerous articles discuss the various surveys performed by the USDA (Borrud, Enns, & Mickle, 1996) as well as the trends in food and nutrient intake that are derived from them (Enns, Goldman, & Cook, 1997). This last referenced article compares the 1977 NFCS, the 1991 CSFII, and the 1995 CSFII. There are two major USDA food intake survey projects. They are the Nationwide Food Consumption Survey (NFCS) and the Continuing Survey of Food Intake by individuals (CFSII). The NFCS is conducted approximately every 10 years with the most recent performed in 1987-1988. It should be noted here that the original food intake model in the 1990 FIPR report came from the Pennington model. This model was derived from two other studies, one of which was the NFCS study. The most recent CFSII was conducted in 1994 -1996. Over the course of the three-year study over 16,000 individuals were queried about their dietary intake on two nonconsecutive days. Obviously, this study produced a large amount of data. These data 20 were separated in much the same way as the EPA data discussed above. This study has more data points than that of the EPA, NRC or RESRAD studies, but it only has essentially 1 1 major food categories and 15 subcategories. Table 3-5 shows these data for a one-day sampling of male respondents. Table 3-5: 1994-1996 CFSII Dietary Intake Data Source Intake Item (gm/day) Total Grain Products 361 Yeast Breads and Rolls 63 Cereals and Pasta 89 Ready to Eat Cereal 16 Mixtures mainly grain 128 Total Vegetables 242 Dark Green Vegetables 14 Deep Yellow Vegetables 8 Tomatoes 37 Total Fruits 172 Citrus Fruits 65 Bananas 19 Non Citrus juices and nectars 19 Total Mlk and milk products 256 Total fluid milk 178 Whole milk 54 Lowfat milk 85 Skim milk 35 Milk Desserts 33 Cheese 18 Total meat, Poultry and Fish 275 Beef 38 Pork 15 Mixtures mainly meat, poulty and Fish 137 Eggs 23 Legumes 31 Nuts and Seeds 4 21 The source of these data, although statistically more accurate in that it came straight from a survey of a large number of respondents, should also be suspect for the simple reason that it is a survey. Surveys have their own inaccuracies due to the people questioned and the method of questioning. Conclusion The above databases show that there are a limited number of choices for a comprehensive source for our diet model. The most promising beside the original diet model, the Pennington dietary intake model, is the USDA 1994-1996 CFSII database. This has the largest number of food groups compared to the other databases. The units, grams per year, are the same as the initial diet model. The Pennington model source was from the United States Department of Agriculture NCF study. This database comes from the same organization and the database is newer with more respondents surveyed. These reasons provide that the final source for the dose estimate program should be either the original Pennington Model or the diet from the USDA CFSII 1994-1996. A newer version of the Pennington model would be ideal, but foregoing this possibility the author chooses to utilize the existing Pennington model minimally updated with data from the CFSII 1994-1996 survey. These data are shown in Table 3-6. Should a newer more complete version of the Pennington model become available another comparison will be performed to determine the most suitable model. Table 3-7 shows the various factors considered in a decision matrix to allow determination of a dietary intake model. Five factors were important considerations. The most important factor was the possibility of similar studies being performed. The initial Pennington model had the dose calculation performed in 1990. The date of publication 22 was the next factor. Two models had more recent publication dates but due to the following three factors were unsuitable. Table 3-6: Dietary Model Intake Source Intake Item (g./day) DAIRY Milk 193 Cheese 18 MEAT Beef 37 Pork 15 Other 217 FISH 14 EGGS 24 CEREAL FOOD Corn Grain 5.18 Grain 4.55 Cereals/Bread 174.7 CAULIFLOWER/BROCCOLI Cauliflower 0.71 Broccoli 2.8 LEAFY/COLE VEGETABLE Cabbage 7.04 Collard Greens 0.45 Lettuce 23.38 Mustard Greens 0.45 Spinach 3.28 Turnip Greens 0.45 Other 0.76 Celery 0.62 LEGUMES Green Peas 7.29 Other Beans 25.71 Nuts 4.94 Other 11.28 Source Intake Item (g./day) SEEDS/GRAINS Blackeyed Peas 5.61 Rice 22.94 Yellow Corn 14.41 TUBERS/ROOTS Carrots 2.92 Onion 4.19 Radish 0.32 Turnip 0.42 Potatoes 85.22 Other 1.1 GARDEN FRUIT Cucumbers 2.62 Greens Beans 8.8 Green Peppers 1.99 Strawberries 1.23 Tomato 25.18 Watermelon 3.44 Yellow Squash/Zucchini 1.26 Other 6.55 TREE FRUIT Citrus Orange 85.26 Grapefruit 7.78 Lemon 10.71 Other 60.36 SOUPS 36.82 CONDIMENTS 54.12 DESSERTS 78.3 BEVERAGE 1172.44 WATER 512 TOTAL 2997.58 23 Table 3-7: Decision Matrix Table Model Similar Studies Date of Publication Source Quality Comparability Pennington 1990 Yes 1990 1987/8 17 and 43 Good NRC NRG 1.109 No 1977 1974 5 or 7 Fair RESRAD No 1989 1977 5 Fair EPA-EFH No 1997 1989/91 — Poor EPAFRG#13 No 1995 1974 — Not The source of each model was examined as the third factor. The EPA Exposure Factor Handbook had the most recent source with the Pennington model second. Quantity, or number of food categories for overall diet and possibility to analyze them, was considered with Pennington having the most complete diet and most available food categories. Both EPA documents in this category were not applicable due to the large number of categories and dietary items. Comparability was considered as the fifth and lowest priority category. This column relates to the format in which the data are presented and similarity of individual studies. As an example, EPA's FGR #13 is in Kcal per day, which is difficult to compare with grams or kilograms per day. The Pennington had good comparability, whiel NRC 1.109 resrad were listed as fair due to having comparable units without a specified individual such as a 25-year-old male. All of this led the author to a determination of an updated Pennington diet model as the best choice for the dietary intake model. A dietary intake model choice is made more difficult due to the fact that it is hard, if not impossible, to define a "normal" individual or diet. This is even more complicated when a limited area such as Florida or Gainesville is chosen. The closest similar previous study to determine individual doses in Florida was the Pennington model. Therefore, an updated Pennington model was chosen. 24 The errors associated with the various diets were not included only the EPA EFH had errors associated with the dietary intake. The analyses performed in the following chapters assign various distributions which include fluctuations, errors, and variability. The distribution for this factor is assumed to be a lognormal due to the facts that dietary intake is a variable in which the individual has a wide latitude of intake and therefore some will exercise this power. Allowing for this fact, the factor was evaluated as a lognormal distribution as well as a normal (gaussian) distribution. The next chapter discusses the results derived from the gamma spectroscopy analysis of the local samples bought and analyzed from the various stores in the Gainesville, Florida, area. CHAPTER 4 EXPERIMENTATION Introduction This is the fourth in a series of seven chapters the overall goal of which is to design and implement a methodology utilizing the Crystal Ball program to determine a statistical value, a number, and associated fluctuation of an individual's radiation dose based on foods bought from local stores in Gainesville, Florida, and to provide comparison through analysis to a similar previous study. This dose will be described not by a singular number but will be expressed as a distribution. This distribution will be determined by a series of analyses, on both the 1990 FIPR diet and a new set of data determined by experimentation utilizing the Crystal Ball program to evaluate the distribution and value of the final dose. Crystal Ball is a forecasting program that is an "add-on" program to Microsoft Excel (Decisioneering, 1996). Initially designed as a financial forecasting program for business analysts, this program has a unique and powerful ability to determine the dose distributions that are under investigation. A Monte Carlo random sampling technique is utilized within the program to determine the distribution of the final outcome. The goal of this chapter is to describe the analysis performed on various samples to determine the concentration and distribution of radionuclides in the foods purchased. This goal will be accomplished in several stages. Previous work and literature search was undertaken to determine what to measure, how to measure it, and what foods to analyze. 25 26 Next, a discussion of the various radionuclides under consideration will be reviewed. Then, the actual experimental analyses will be described. Four separate analyses were performed to measure the concentration of radionuclide concentration in food. The four analyses will be described along with the information obtained. The conclusion will consolidate all the data Initial Store Samples Literature Search The literature search described in the second chapter of this series described the previous samples taken from various locations to assess the radionuclide concentrations in foods grown in several regions around the world. The focus of this chapter was necessarily limited to a study of radionuclide concentration of foods in Florida. The additional sources of literature provided useful comparisons on the various radionuclides considered, the diets studied, and the methods of analyses. There are three sources that provided information both for the dietary model and the initial concentration of radionuclides in food grown on phosphate and related lands. The first document is the 1986 FIPR report that provided the initial analysis of radium- 226, lead-210, and polonium-210 in foods grown on phosphate lands (Guidry et al., 1986). Other radionuclides were also examined in these data. The diet model that describes dietary intake was first presented in this document. The method of analysis and the dose evaluation were described in this book. Simplified analysis of radionuclide concentration in foods was performed to determine dose to an individual. Three types of individuals were considered: control, local, and maximum. 27 The next two documents were associated with this initial document. Brian Birky's master's thesis referred to the previous document and used the same methodology, diet, and radionuclides to determine dose attributable to technological enhancement of this phosphate-reclaimed land (Birky, 1990). Birky (1990) detailed the previous methods and studies that were utilized to prepare, enclose, and measure the experimental samples. Additionally, the methodology utilized to calculate the dose to an individual directly from the dietary intake spreadsheet was explained. The explanation was much more descriptive in the details of diet and dose calculation than the initial chapter. Guidry et al. (1990) conducted a continuing study based on the recommendations of the 1986 FIPR paper. The same basic dietary intake model was used as that considered in Guidry et al. (1986). The same radionuclides were considered. Three radionuclides and five land types were examined. Three types of individuals were considered in this paper also: local, control, and maximum. The basic dietary model, with few revisions, was presented in this paper. The differences in the data were analyzed. Regression analysis was performed on the collected data. More data points were added from the previous study, and more analyses were performed that detailed the soil to plant transfer model and refined the dietary intake model. FIPR has continued to improve its database with more samples since this report, and the extended database will be available in a publication in the near future. The current research and work also has continued to smooth the statistical data. These chapters primarily discuss the various analyses performed on foods grown on Florida lands in general and phosphate lands in Florida in particular and are the most useful and pertinent to this study. 28 The concentration of radionuclides in food has been studied in several areas and contexts. The previous three chapters discussed this very subject and determined the concentration of several radionuclides in various foods grown on phosphate-related lands. To provide for data for this report, and as a means of comparison for the previous report, similar samples were taken from local stores. This chapter will discuss the radionuclide considerations, the stores utilized, the samples taken, the method of measurement, and the results of the measurements. Radionuclide Considerations Three radionuclides were considered consistently in the previous reports: lead- 210, radium-226, and polonium-210. Each of these is of concern for various reasons. All are from the uranium decay chain, and two are progeny of radium-226. The lead-210 and radium-226 radionuclides will be discussed in turn. Lead-210 (Pb-2 10) This radionuclide is a progeny of radium-226 through decay of radon-222. Lead-210, unlike radon, is a reactive radioisotope that adsorb onto particulates and therefore pose a possible risk to humans through ingestion and inhalation. Most environmental lead is associated with sediments, and the rest is in dissolved form. Short-term exposure to even low levels can cause changes in red blood cell chemistry; developmental problems; and attention span, hearing and hearing and learning disabilities in children. Adult short-term exposure can cause a slight increase in blood pressure. Long-term exposure has been linked to cerebrovascular and kidney disease (Weiner, 2000, pp. 221, 222). Environmental and toxic considerations aside, a large fraction of the lead-210 in the environment have been formed following the decay of radon-222. Therefore, higher 29 concentrations of lead-210 are found in the surface soils. This increases the chance of intake through the human food chain adding to an individual's dose (Harley, 1988). Additionally, lead was analyzed in the previous FIPR studies and provides a point of comparison for the experimental data obtained in this study. Radium-226 fRa-226) There are more data on this radionuclide than on any other radionuclide. Inhalation of radon daughters account for 55% of the human exposure to natural sources of radiation (Shleien et al., 1998). Radium toxicity is related to bone sarcomas and sinus sarcomas due to its competition for bone with calcium. These factors as well as the fact that the FIPR database includes this radionuclide led to the consideration of radium-226 as one of the points for analysis in this study. Original versus New Database There are two databases that could have been considered from the FIPR studies of the previous radionuclides. The original database from the 1990 FIPR report was chosen because the newer database has not been completed, confirmed, or published. The original database considered all three radionuclides and the diet model and has been in the literature numerous years. These reasons led to inclusion and comparison of the original database. Samples Considered The March 1986 FIPR report analyzed over 100 food samples, replicated up to three times, collected from 62 land parcels. The Phase 2 1990 FIPR report initial report collected and evaluated approximately 70 samples from five land parcels. These samples 30 were considered to determine the samples to evaluate from the stores. The samples are listed in Table 4-1. Table 4-1 : Food Samples Analyzed from Local Grocery Stores Beef 1 Beef Kidney 1 Black-Eyed Peas 3 Brazil Nuts 1 Brazil Nuts Shells 1 Broccoli 3 Cabbage 3 Carrots 3 Cauliflower 3 Collard Greens 3 Corn 3 Cucumber 3 Eggplant 3 Grapefruit 3 Green Beans 3 Greens Onions 3 Green Peppers 3 Irish Creamer Potatoes 1 Lemons 3 Lettuce 3 Lima Beans 3 Mustard Greens 1 Okra 3 Onions 5 Oranges 3 Parsley 3 Peas 3 Pole Beans 2 Potatoes 3 Purple Hull Peas 2 Radishes 2 Red Potatoes 2 Rice ■5 Spinach Strawberries -> Swiss Chard 1 Tangerine 2 Tomatoes 3 Turnip Greens 3 Turnip Roots and Greens 1 Turnip Roots 2 Watermelon 2 Yellow Corn Yellow Squash "5 Zucchini 3 Total 113 The samples taken ranged from beef to zucchini. There were 1 13 samples total; 45 foods were sampled. A sample is considered as a 0.5 marinela beaker filled with the food in question. Eight foods had only one sample; 6 foods had two samples; and the remainder of the foods, 31, had three samples. This provided a good average for each food from the three stores. Samples were bought from three stores in the local area to provide a better statistical analysis. Samples were purchased from large supermarkets to increase the 31 usefulness of this analysis. People outside the Gainesville area and the state of Florida could utilize these same data in other areas of the country. The first set of samples was purchased from Publix at 5200 NW 43 rd Street on 12 August 2000. Albertsons at 3930 SW Archer Road was the site where the second set of samples was purchased on 13 October 2000. The third store was Winn Dixie at 7303 NW 4 th Boulevard where the third set of samples was purchased on 20 December 2000. It is important to note that some of the samples only had one or two replicates. This was usually due to the limited availability of samples due to their seasonality. Location of Samples The samples were purchased from the various stores listed above. The question that should be considered is where they were grown. This is an important factor due to soil contamination, plant uptake, and therefore plant contamination. Samples from each individual store come from numerous samples, which often change daily (Greg Sciullo, personal communication, 30 October 2000). Even if a purchaser asks on the day the food is bought, the store can usually only provide the supplier and region and not the location at which the food was grown. This is why it is important to do this and follow-up studies that consider exact sources and their soil radioactivity as well as plant uptake and human consumption availability. Brazil Nuts Brazil nuts and Brazil nut shells were actually the first product bought sealed and studied. Of all the samples examined, they had the most number of peaks although not all were identifiable. 32 Food Preparation All foods were prepared as for normal human consumption. No foods were cooked, and food was cleaned, cut, and sliced to fill individual containers to maximize weight. The foods were then fit into a 0.5-liter Marinelli beaker. The beaker was capped, sealed, and stored for two weeks to allow ingrowth of radon-222 and its daughter products to equilibrium with its parent radium-226. The sample was then weighed and counted on one of two high-resolution gamma ray spectrometers. The scale that samples were weighed on was a Mettler P2000N, Serial No. 394916. Detectors 2 and 4 were used for the analysis. Detector 2 is a Germanium well detector, Serial No. 22P63XC, University Property No. 491044 1100485. Also, a Germanium well detector, Serial No. 1284121 1302, University Property No. 4910 AA 1 17706, is the University Property No. for Detector 4. The count time varied from 9 to 24 hours. Most samples were counted for 9.5 hours. Sampled items were counted on only two of four detectors available. This was due to consistency of only using two detectors as well as the limited availability of the other detectors. Grocery Store Analysis After gamma counting the samples utilizing detectors 2 and 4 in the Environ- mental Engineering Sciences laboratory, a peak search was performed. Each spectrum was visually inspected for additional peaks that the library search did not recognize. Radionuclides Evaluated The 1990 FIPR study evaluated their samples for three radionuclides. This analysis considered the same three radionuclides because they are from the U-decay 33 series and have identifiable peaks when counted on a gamma spectroscopy system. These are associated with phosphate mining and are exposed to the surface and therefore may be taken up by plants (Guidry et al., 1986). Radium-226 decays through several short- lived isotopes to radon-222. Radon is a gas that accumulates in structures and can provide a significant contribution to an individual's dose. Radium-226 CRa-226) The radium content was calculated by summing the three peaks at 295.2, 352.0, and 609.4 keV. These peaks are from the Pb-210 and Bi-214 daughters. The results are reported in pCi/gm of material measured (pCi/g) Lead-210 (Tb-210^) The lead-210 content was calculated utilizing the 10.8 keV peak activity. The results are reported in pCi/gm of material measured (pCi/g). Potassium-40 (K-40) The potassium-40 (K-40) radionuclide was measured, and data are available for analysis but are not reported in this chapter due to the fact that they were not analyzed in the FIPR 1986 or 1990 report and therefore have little use in a comparison methodology. It is interesting to note that the 1460keV potassium-40 peak was present and easily identifiable in a majority of the samples. Correction Factor A correction factor based on the detector, the radionuclide, and the 45 13 standard was calculated. The standard has an activity of 33200 pCi. The correction factor was 34 determined for radium-226 by combining the counts from the three peaks: lead-214 (295 KeV), lead-214 (352 KeV), and the Bi-214 (609 KeV) and dividing this sum by the time to obtain the rate of the sample in counts per second (cps). The equation for the calibration factor is shown below: Calibration factor (CF) = 4513 Activity /Measured count rate (Equation 4-1) The calibration factors were calculated and are shown in Table 4-2. Table 4-2: Compilation of Calibration Factors Pb-210 (PCi/cps) Ra-226 (Pci/cps) Detector 2 3.40E+05 1670 Detector 4 1.10E+05 1664 Calculation Once the counts for each sample were analyzed and the blank sample counts were subtracted, the number was multiplied by the correction factor and divided by the weight to obtain the answer in pCi/gram. The calculation is shown below: Concentration = (Sample (cps)-Background (cps))*CF/Weight (Equation 4-2) Minimum Detectable Activity Many of the samples returned values of zero at several of the peaks examined. The minimum detectable activity was calculated at each of these data points and reported as the actual activity. This methodology provides for a conservative dose analysis as well as providing a more complete analysis. 35 A calculation of minimum detectable concentration (MDC) is calculated by first calculating the limit of detection (LD), as shown below in Equation 4-3. Limit of Detection (LD) = 2.83 * ((Blank/(time)) m (Equation 4-3) The MDC is then calculated using the Equation 4-4. MDC (pCi/gm) - LD (cps) * CF (pCi/cps)/Weight (g) (Equation 4-4) Once these data were calculated, they were reported in the data as the counts. Output of Analysis Figure 4-1 shows a sample output from the Gamma Vision Program utilized to count the various samples. An output report similar to this one was produced for each individual sample. A spectrum was also printed out to allow a visual observation and comparison with other samples. Detector #4 ACQ 09-Sep- 00 at 9:05 :03 RT = 34200 LT = 34187.1 Detector # 4 HPGe End Cap in Green Shield Beef 09/09/2000 ROI# RANGE ( keV) GROSS NET CENTROID FWHM FW(1/10) LIBRARY ( keV) Bq 1 72.11 79.55 1190 297 71 76.91 59 1.35 No close library match . 2 256.31 261.13 354 -25 34 258.66 C 3? 0.71 No close library match. 3 522.34 526.95 457 221 30 524.76 65 2.91 No close library match. 4 623.75 626.36 145 56 13 624.77 1 22 1.74 No close library match. 5 1492.05 1497.04 959 768 37 1494.45 2 11 3.73 No close library match. Figure 4-1 : Sample Report for Beef Results and Analysis Appendix A illustrates, in tabular form, the raw data that provided the dose determination. Peak information was determined from reports similar to Figure 4-1 . These were output from the library search performed on each spectrum measured from 36 each sample. Appendix B contains the Crystal Ball analysis charts for the various analyses performed. Table 4-3 lists the results for this analysis. As can be observed from these data, cucumbers show the highest lead-210 concentration at 47 pCi/g. Beef was observed to have the lowest lead-210 concentration at 0.076 pCi/g. Potatoes, rice, beef kidney, and watermelon show the lowest radium-226 concentration with 0.002 pCi/g. Parsley had the highest observed concentration at 0.029 pCi/g. Table 4-3: Gamma Spectroscopy Analysis of Local Grocery Samples Averages (pCi/g) Item Pb-210 Ra-226 Beef 0.076 0.004 Beef Kidney 0.357 0.002 Black-Eyed Peas 0.494 0.003 Brazil Shells 1.021 0.003 Broccoli 0.829 0.005 Cabbage 0.858 0.006 Carrots 0.555 0.004 Cauliflower 1.466 0.005 Collard Greens 1.372 0.006 Corn 0.506 0.006 Cucumber 47.082 0.009 Eggplant 1.425 0.006 Grapefruit 0.096 0.005 Green Beans 3.837 0.007 Green Onions 0.852 0.014 Green Peppers 0.431 0.004 Irish Creamer Potatoes 0.120 0.006 Lemons 0.414 0.005 Lettuce 1.237 0.004 Lima Beans 0.963 0.003 Mustard Greens 1.622 0.017 Okra 1.072 0.003 Onions 0.599 0.004 Averages (pCi/g) Item Pb-210 Ra-226 Oranges 0.682 0.003 Parsley 7.378 0.029 Peas 0.821 0.003 Pole Beans 0.704 0.004 Potatoes 0.846 0.002 Purple Hull Peas 0.454 0.003 Radishes 0.580 0.004 Red Potatoes 0.215 0.003 Rice 0.654 0.002 Spinach 0.422 0.020 Strawberries 0.715 0.004 Swiss Chard 2.010 0.006 Tangerine 0.686 0.004 Tomatoes 1.011 0.003 Turnip Greens 0.941 0.006 Turnip Root and Green 1.841 0.005 Turnip Roots 0.941 0.006 Watermelon 0.776 0.002 Yellow Corn 0.680 0.005 Yellow Squash 0.613 0.004 Zucchini 0.108 0.005 Brazil Nuts 1.324 0.007 37 The average for lead-210 for all samples is 2.037 pCi/g. This value is higher than most due to the largest value increasing the value. All of the samples have concentrations below this value with the exception of parsley and cucumber. The average for Ra-226 is 0.006 pCi/g. Fifteen sample concentrations lie on or above this value with all others measured below. Brazil nuts and their shells cause this value to be higher than most of the measured values. The concentration of mustard greens lies at this value, and all other concentrations lie below this value. Rice Experimental Analysis Determination of the distribution associated with the concentration of radionuclides in food was undertaken with the following results. The distribution of a radionuclide concentration in a food was approached utilizing two major methods: experimentally and with a review of relevant literature current studies. Review of Literature and Current Studies The 1986 FIPR report initially assumed a lognormal distribution. The subsequent pilot study and analyses utilizing a residual test bore out this hypothesis. This was performed primarily for radium-226 in the various food items for the study. The study analyzed 3 1 food items in six general categories. The subsequent 1990 study and the current research agree with the initial analysis from the 1986 paper. The findings were for a lognormal distribution, which was determined by analyses of the data distribution for specific food items grown on each land analyzed for each radionuclide. 38 Experimental Analysis Even though these data seem conclusive in one method to assume a lognormal distribution, they do not address the point of different food items, especially the grocery items. This chapter deals with research performed on grocery store items, whereas the previous studies did not. The 1990 FIPR report (Guidry et al., 1990) analyzed one sample of each food type but could not perform any relevant or applicable analyses on only that one data point. This chapter dealt with 3 data points (in most cases) from each food type. An analysis was undertaken to analyze a food type for the distribution. The results obtained, although numerical in nature, were essentially qualitative. The determination of distribution was obtained through measurement and analysis of rice obtained from Publix and measured for a single radionuclide. Choice of Food Sample The rice was purchased from Publix on 4 February 2001. The brand chosen was Publix' own brand. This was chosen both for the price consideration as well as the probability of consumption due to the limited cost by an average consumer. Rice was chosen also because it provided a consistently high potassium-40 peak on prior analyses. This provided a good indication that this sample would provide a good consistent peak to analyze on all samples measured. Preparation Similar to all the experimental analysis for this research, the 20 samples of rice were placed in Marinelli beakers. Each 0.5 beaker was filled with rice, sealed and refrigerated for two weeks to allow for ingrowths of the Radon daughters to equilibrium. 39 Measurement The samples were weighed after the two-week period. Each sample was then measured on one of two high purity GeLi detectors. Detectors 2 and 4 were chosen for this analysis due to their previous utilization with other samples as well as their availability. The samples were each measured for 9-1/2 hours. Once again, this time was chosen to provide an opportunity for future comparison with other data obtained in this research. Comparison The spectrums of the samples, once counted, were individually examined to ensure the potassium-40 peak was observed and analyzed. As expected, the peak was found on every sample to varying degrees. An analysis of the data was performed on the 10 samples measured on each detector as well as overall for all 20 samples. Results These data were analyzed for several statistical attributes, such as skewness, maximum, minimum, kurtosis, range, and standard deviation. Tables 4-4, 4-5, and 4-6 show the summary statistics for detector 2 and detector 4. A comparison of the raw data and these numbers illustrate that one point on detector 4 was an outlier. Tables 4-7 and 4- 8 show the same statistical comparisons for the combined data with and without the outlier, respectively. A survey of the statistics from detector 2 (Table 4-4) shows that the range of counts per second per gram for the samples measured was 3.36 * 10" 6 . The mean of all samples on these detectors was 5.83 *10" 6 . The standard deviation was 1 *10" 6 . The 40 skewness, a measure of the distribution to deviate from a standard distribution, is 0.378. This supports the contention of the literature cited above that states that the distribution of radionuclide concentration of food is lognormal, in this case positively skewed. Table 4-4: Summary of Rice Sample Statistics from Detector 2 SUMMARY STATISTICS DETECTOR 2 Mean Standard Error Median Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Largest (1) Smallest (1) Confidence Level (95.0%) 5.82591E-06 3.18389E-07 5.71661E-06 1.00684E-06 1.01372E-12 -0.165870891 0.378137914 3.36092E-06 4.26156E-06 7.62247E-06 5.82591E-05 10 7.62247E-06 4.26156E-06 7.20248E-07 Table 4-5 shows similar statistics for the samples measured on detector 4. The outlier is included in this analysis for the sake of comparison and to illustrate the effect that the outlier has on the analysis. The mean of the data with the outlier is 5.05*10" 6 . The standard deviation is 1.6 *10" 6 . The range is 5.96* 10" 6 . This number is close to twice as large as the range associated with detector two samples. The mean was measured as S.OS'MO" 6 and the skewness as -1.25*10" 6 . This is not only larger but in the opposite 41 direction to the distributions both researched and assumed. An observation of the raw data illustrated that one data point, 1 .3* 1 0" 6 was an outlier. Once this was removed, Table 4-6 was obtained and analyzed. Table 4-5: Summary of Rice Sample Statistics from Detector 4 SUMMARY STATISTICS OF RICE SAMPLES ON DETECTOR 4 Mean Standard Error Median Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Largest (1) Smallest (1) Confidence Level (95.0%) 5.05372E-06 5.16785E-07 5.21956E-06 1.63422E-06 2.67067E-12 2.670178378 -1.254131791 5.96386E-06 1.29724E-06 7.261 1E-06 5.05372E-05 10 7.261 1E-06 1.29724E-06 1.16905E-06 Table 4-6 illustrates that with the outlier removed, the mean is now higher at 5.5 *10" 6 . The standard deviation has now been reduced to 1.02*10" 6 . The range is now 3.25 * 10" 6 , less than detector 2. The skewness measured a +0.37, which is very close to that measured for detector 2. These data, with the outlier removed, tend toward a lognormal distribution due to the skewness measured and the similarity of data obtained from both sets of samples. 42 Table 4-6: Summary of Rice Sample Statistics without Outlier from Detector 4 SUMMARY STATISTICS ON DET 4 WITHOUT OUTLIER Mean Standard Error Median Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Largest (1) Smallest (1) Confidence Level (95.0%) 5.471 11E-06 3.40689E-07 5.52044E-06 1.02207E-06 1.04462E-12 -0.449095314 0.37326003 3.25132E-06 4.00978E-06 7.261 1E-06 4.924E-05 9 7.261 1E-06 4.00978E-06 7.8563 1E-07 An analysis was undertaken to compare the same statistics on both data sets combined. There were two analyses performed, one with the outlier and one without the outlier. These are shown in Table 4-7 and 4-8. Table 4-7 illustrates the summary statistics on the rice samples measured from both detectors combined. Consideration of the outlier would provide a mean of 5.4* 10" 6 . A standard deviation would be obtained that would be 1 .38* 10" 6 . The range would be 6.3* 10" 6 with the minimum and maximum measured at 1.3*10" 6 and 7.6* 10" 6 , respectively. The skewness would be a - 1 .2* 1 0" 6 . All of this, as well as the data from detector 4 above, details a reasonable justification for removing the outlier and considering the other 19 data points as the total sample. 43 Table 4-7: Summary of Rice Sample Statistics: Total Rice Samples STATISTICS-ALL DATA POINTS "" Mean 5.43981E-06 Standard Error 3.08395E-07 Median 5.49973E-06 Standard Deviation 1 .3791 8E-06 Sample Variance 1.90215E-12 Kurtosis 3.328489995 Skewness -1.201595498 Range 6.32524E-06 Minimum 1.29724E-06 Maximum 7.62247E-06 Sum 0.000108796 Count 20 Largest (1) 7.62247E-06 Smallest (1) 1.29724E-06 Confidence Level (95.0%) 6.45478E-07 Utilizing the other 19 data points and performing a summary analysis, Table 4-8 is obtained. As can be observed from Table 4-8, similar to the observations from Table 4- 6, the mean has now increased to 5.7* 10" 6 . The standard deviation has now decreased to 1.0* 10" 6 . The range, S.6*^" 6 is essentially half of that obtained with the outlier in Table 4-7, and the skewness was increased to a positive 0.32* 10" 6 , once again supporting the data obtained by the two sources in the literature search from analyses of previous data. Histogram Analysis A histogram analysis was performed on the various sets of data prior to the summary statistics that were derived above. These initial analyses were performed to provide a visual representation of the data and their subsequent distributions. They have been included here to provide for a more complete data analysis as well as to show how the outlier was initially found. Figure 4-2 shows the data plotted in a histogram. The 44 outlier lies to the left-hand side of the plot, conspicuously alone. Further consideration required determination of which detector and sample this number was obtained. Table 4-8: Summary of Rice Sample Statistics: Total Rice Samples without Outlier COMBINED STATS EXCLUDING OUTLIER Mean 5.65784E-06 Standard Error 2.29904E-07 Median 5.52044E-06 Standard Deviation 1 .002 1 3E-06 Sample Variance 1 .00426E- 1 2 Kurtosis -0.512673412 Skewness 0.318703287 Range 3.61269E-06 Minimum 4.00978E-06 Maximum 7.62247E-06 Sum 0.000107499 Count 19 Largest (1) 7.62247E-06 Smallest (1) 4.00978E-06 Confidence Level (95.0%) 4.8301 1E-07 Figures 4-3 and 4-4 show Detector 2 and 4 rice sample histograms, respectively. Figure 4-3 shows all data in a close grouping and range, whereas the histogram of detector 4 has a similar grouping with the notable exception of one data point. The detector 4 histogram has a larger range than that presented on the histogram of detector 2. The grouping of detector 2 has a much smaller range when the outlier is excluded. This was the first indication that there was a point that should be removed in the consideration of the data. Removing this data point and replotting detector 4 rice samples in a histogram reveals Figure 4-5. 45 This histogram reveals the reduced range similar to that obtained with the samples from detector 2. The grouping could be lognormal or normal. A histogram of all samples as well as a statistical summary analyses performed above is a more accurate indicator of distribution. Figure 4-6 shows the histogram of the entire data set with the exception of the outlier. Histogram of AD Rice Samples *t.o - 4- 3.5- 3- 2.5- 2- 1.5- 1 - 0.5- 0- o c 0) 3 ? 1 1 U. I H 1 1 — 1 ! ' 1 1 r™ -i 1 1 1 1 1 M i B i i ■ ___■_■_ | | t 1 1 * r*> .<£ c* rfc & ,& .& fJ •.• SSSJ ^ J ^ <? o* *~ <D V <b V A V %? <* Counts/Second/Gram ^ ^ Figure 4-2: Histogram of All Rice Samples 3.5 3 2.5 § 2 1 1-5 £ 1 0.5 Histogram Detector 2 *& <,& ,& C# & & <b- ^ <& & A-' .# Counts/Second/Gram «* • Figure 4-3: Histogram of Detector 2 Samples 46 3.5 3 j? 2.5 I 2 I 1.5 u. 1 0.5 i.g.| ~ Histogram Detector 4 Counts/Second/Gram Figure 4-4: Histogram of Detector 4 Samples ^ / / / / /' / J" * 3.5 3 2.5 2 g" 15 u. >» o c 0) 3 1 0.5 Histogram Detector 4 excludhg outlet E 1 # J§> I » J* C? rK> <£> rS> <S J- / /" / /" /■ / ^ /" Counts/Secontf G ram Figure 4-5: Histogram of Rice Samples on Detector 4 excluding Outlier. This curve illustrates a bimodal distribution around 6*10" 6 counts/gram/sec and has a slightly lognormal appearance. The distribution at this point was determined using the summary statistical analysis to ensure that the outlier removal was justified and to 47 determine the shape of the distribution. Additionally, the data were analyzed using the Crystal Ball program to determine that the distribution, though limited in number of data points, most closely approximates a lognormal distribution. Histogram of All Rice Samples f j? • Counts/Second/Gram Figure 4-6: Histogram of All Samples excluding Outlier Conclusion and Recommendations for Future Research Analyses were performed on 20 rice samples obtained from Publix Supermarket in Gainesville, Florida. The 20 samples were tested on detector 2 and detector 4 of the gamma spectroscopy laboratory at the environmental Engineering Sciences Department at the University of Florida. The goal of this portion of the research was to determine qualitatively what type of distribution is exhibited by concentration of radionuclides in foods. A literature search was performed providing information specific to foods grown on phosphate related lands. These data stated that the distribution followed a lognormal distribution. The analyses on these samples, with histograms and summary statistics, proved that one of the data points was an outlier and, when excluded, provided good 48 agreement with the data obtained from the previous research. The concentration of radionuclide in food studied in this set of analyses followed a lognormal distribution. Further research should be undertaken, both in the form of a literature search and experimentally, to determine if this is accurate for a wider range of foods. Studies should be performed to determine how the distribution changes by store, location, and land type. Additionally, the data presented here should also be examined utilizing the residuals method to confirm, with another method, how the data best fit this distribution. Another analysis, with more data points, should be undertaken to determine the distribution with better accuracy. The above experimental data on grocery store foods was determined utilizing previous studies as a template as well as a guideline to choose which samples to measure. Brazil nuts, although not in the original work, prove to be hyper accumulators. They exhibit the highest number of peaks of any measured food. Their shells also exhibit the same properties. Beef and beef kidney are only one data point and will not be used for the analysis to follow. An interesting point to note about beef is that it illustrates a low lead- 210 concentration whereas the kidney shows a high lead-210 concentration. The data examined as a whole illustrate that the concentration of radium-226 is lower, on average, than lead-210. This chapter has laid down the concentration and associated distributions of various radionuclides in specific grocery store foods. The previous chapter determined dietary intake and the distribution that it is estimated to follow. The next in this series of chapters deals with the dose conversion factor. The data from these three chapters will be 49 combined in the sixth chapter on dose to provide a more accurate estimate both in number and shape of distribution than currently available in the literature. CHAPTER 5 DOSE CONVERSION FACTORS Introduction This is the fifth in a series of chapters designed to design and implement a methodology to determine a probabilistic radiation dose to individuals from foods bought at local stores in Gainesville, Florida, using the Crystal Ball program. The first chapter provided the introduction of a probabilistic dose approach. The second chapter described the literature search for the overall dissertation to determine the references that were used for each section. The third chapter determined the dietary intake values to be used and the most probable distribution to describe them. The fourth chapter described the actual experimentation performed to determine both the concentration of specific radionuclides in the various foods measured and the distribution to describe this concentration. The purpose of this chapter is to determine the value and distribution to describe the dose conversion factor. Literature Search A literature search was performed to determine the various applicable references in an effort to determine the correct dose conversion factor (DCF) as well as a distribution to apply to it. The data for the dose conversion factor (DCF) came from four sources. The first source was Federal Regulatory Guide number 1 1 (EPA, 1988). This document provides the methodology used to calculate the DCFs for inhalation 50 51 submersion, and ingestion. The tables of the various DCF data for various radionuclides are included in this manual. The articles International Council on Radiation Protection (ICRP) 68 (ICRP, 1994) and 72 (ICRP, 1996) provide age-dependent DCFs for workers and members of the public from intake of radionuclides. The fourth reference for these data was a solution manual that calculated a dose conversion factor for strontium 90 (Turner, Bogard, Hunt, & Rhea, 1988, pp. 96-101). This was utilized as a reference to describe the method to obtain a dose per unit intake factor from the initial data. It should be noted that an additional vital source of information describing the distribution was a direct conversation with Dr. Eckerman at Oak Ridge National Laboratories. He provided the data that stated that the dose conversion factors follow a lognormal distribution. Lead-210 and radium-226 distribution encompass 90% of the values by multiplying and dividing the mean by a factor of five. Polonium-210 distribution can encompass 90% of the values by multiplication and division of the mean by a factor of 10. These data were incorporated into the final analysis of each dose analysis as the ninth case. Discussion There are two points which need to be addressed at this point: the distribution and the method to obtain or make an educated estimate and the different sources of DCFs. Either a distribution can be assumed or it can be calculated utilizing the Crystal Ball analysis to assign distributions to each of the variables in the equation. Either approach will produce a final output that will be utilized in the next chapter to calculate 52 and derive a distribution for the end product dose. The purpose of this chapter is to derive a probabilistic methodology that can predict a distribution for dose. There are at least three different sources of dose per unit intake or dose conversion factors: the EPA Federal Regulatory guide (FRG) number 11, International Council on Radiation Protection (ICRP) Publication 68 and ICRP 72. These sources and their DCFs are listed in Table 5-1. Table 5-1: Dose conversion Factors from Various Sources (Sv/Bq) ICRP 68 ICRP 72 FRG 11 Pb-210 6.80e-7 6.90e-7 1.450e-6 Ra-226 2.80e-7 2.80e-7 3.58e-7 Po-210 2.40e-7 1.20e-6 5.14e-7 As can be seen from this table, the numbers are not identical and have a rather large variance. The dose conversion factors from Federal Regulatory Guide Number 1 1 were utilized in this report. These data were chosen to maintain consistency with previous reports and to provide comparability with data from those same reports. Conclusion and Recommendations The above data for the EPA FRG number 1 1 will be utilized for the purpose of this report with the distribution to be assigned as a lognormal distribution. The EPA FRG 1 1 dose conversion factors will be converted to mrem/pCi to maintain consistency and units. A suggestion for future work is twofold. The discrepancies between the various agencies and their dose per unit intake should be considered and evaluated. Additionally, the distribution for this factor should be evaluated utilizing Crystal Ball 53 and the individual factors in the equation to obtain a more accurate determination of the distribution for this factor. The next chapter combines all the previous data and distributions together. The original 1990 FIPR (Guidry et al., 1990) study is analyzed for a series of distributions for each of the parameters. Two radionuclides are considered: radium-226 and lead-210. The resulting Crystal Ball dose distributions are presented in tabular format. A similar analysis is performed on the grocery store data for each radionuclide. The last chapter sums all the previous data into a combined whole for comparison and discussion. CHAPTER 6 COMMITTED EFFECTIVE DOSE EQUIVALENT Introduction This chapter designed to determine and test a methodology to calculate a probabilistic radiation dose to individuals from foods bought at local stores in Gainesville, Florida. The first chapter provided the introduction of a probabilistic dose approach. The second chapter described the literature search for the overall dissertation to determine the references that were used for each section. The third chapter determined the dietary intake values to be used and the most probable distribution to describe them. The fourth chapter described the actual experimentation performed to determine both the concentration of specific radionuclides in the various foods measured and the distribution to describe this concentration. The fifth chapter described the methodology to determine the dose conversion factor (DCF) value and distribution. The purpose of this chapter is to determine the value and distribution to describe the dose to an individual based on the values obtained in the previous chapters. This purpose will be accomplished by a literature search that describes the applicable and relevant literature to determine the committed effective dose equivalent, the term to describe the extended dose to an individual based on intake of a specific radionuclide. The data previously obtained were then analyzed with the original data and comparison is provided. 54 55 Literature Search Dose to an individual can be calculated in several ways. The EPA Federal Regulatory Guide Number 1 1 provides the dose conversion factors utilized in this chapter (EPA, 1988). Other dose conversion factors from ICRP 68 (ICRP, 1994) and ICRP 72 (ICRP, 1996) were considered but not utilized for this analysis. This was to maintain consistency from the previous 1990 Florida Institute of Phosphate Research (FIPR) report. These tables allow the user to calculate a dose to an individual based on the individual's unit intake of a radionuclide. The 1990 FIPR report was utilized for its diet model and dose analysis of radium- 226 and lead-210 (Guidry et al., 1990). The dose analysis from this report was utilized to determine the associate dose and distribution to a known and published value for a diet of an individual living in Florida. The dose model considered from this paper was only the debris land model for each radionuclide owing to the fact that the maximum individual in this category had the highest dose. Method Determination of dose to an individual is accomplished by integrating the information determined in the previous papers, multiplying the appropriate factors, summing, and then running Crystal Ball on the entire set to determine an output. Equation 1-1 illustrates the formula to calculate dose to an individual. Each variable in this formula is assigned a value in a Microsoft Excel spreadsheet. The various values for intake, concentration, and dose conversion factors are assigned a distribution from the Crystal Ball library. Crystal Ball, produced by Decisioneering, is a program addition to Microsoft Excel (Decisioneering, 1996). This program utilizes a Monte Carlo sampling 56 technique for each assigned distribution to determine a final dose in the form of a distribution. Monte Carlo is a method in which a random sample is picked from each distribution and used in the calculation. Each random sampling, with its resultant output, is called a trial. Depending on the number of trials specified, an output distribution is framed. The more trials performed, the more accurate the distribution. Specific fluctuations in the variables such as location of individuals, eating habits, land type, where food is grown, radiation type and food preparation methods are taken into account by the distribution determination in each variable. Specific errors are considered as a whole to contribute to the shape of the distribution. A family of distributions and analyses are performed to ensure flexibility of the resultant output in determination of a final dose. Should one specific set not be correct in its distribution choice, other sets will allow the correct determination of dose and associated distribution. Nine sets of analyses were performed on each radionuclide, lead-210, and radium- 226. These analyses were performed on the original 1990 FIPR report and the experimentally obtained grocery store data. The data are presented in tabular format, comparing the different distributions uses and the different distributions obtained for each set. The sets of data are presented below in Table 6-1 . The various sets each have different values for intake, concentration, and dose conversion factors. LN represents a lognormal distribution, and G represents a gaussian distribution. The intake values for each variable were obtained from the previous chapters. The intake values were obtained from the 1990 FIPR report and the third report 57 in this series. The concentration data were taken from the fourth chapter, the experimental analyses on the grocery store samples and from the 1990 FIPR report. The dose conversion factors were obtained from Federal Regulatory Guide #11. Default values were utilized for the various parameters that could not be identified. Set nine is a special case that is similar to set 1 with the exception that the dose conversion factor is specified by a more exact representation of the actual DCF. Set 9 is the most plausible scenario for the dose value and distribution. All Crystal Ball analyses were run with 20,000 trials to improve consistency, accuracy, and comparability. Table 6-1 : Sets of Distributions Utilized in Analyses on Data Intake Concentration DCF Set 1 LN LN LN Set 2 G LN LN Set 3 G G LN Set 4 G G G Set 5 LN G G Set 6 LN LN G Set 7 LN G LN Set 8 G LN G Set 9 LN LN LN Analysis of 1990 FIPR Dose Diet Radium 226 Analysis on 1990 FIPR Data The dose worksheet provided in Table 6-2 shows the spreadsheet for the radium- 226 dose calculation that was used as input to the Crystal Ball program. Each of the intake variables and concentration variables were assigned a distribution. The dose 58 Table 6-2: Input Spreadsheet Data for Radium 226 Dose Calculation (Guidry et al., 1990) DCF 1.30E-03 (mrem/pCi) Diet Item Intake (g/day) Concentration (pCi/kg) Intake (PCi/yr) Broccoli 3.51 34.67 44.42 LEAFY Cabbage 7.04 32.2 82.74 Collard Greens 0.45 86.23 14.16 Lettuce 23.38 45.41 387.52 Mustard Greens 0.45 64.22 10.55 Spinach 3.28 540.25 646.79 Turnip Greens 0.45 55.47 9.11 SEEDS/GRAINS Blackeyed Peas 5.61 25.6 52.42 Rice 22.94 82.18 688.10 Yellow Corn 14.41 25.6 134.65 ROOTS Carrot 2.92 113.83 121.32 Onion 4.19 33.3 50.93 Radish 0.32 33.3 3.89 Turnip 0.42 23.64 3.62 GENERAL Cucumber 2.62 18.6 17.79 Green Beans 8.8 9.79 31.45 Green Peppers 1.99 18.6 13.51 Strawberries 1.23 806.68 362.16 Tomato 25.18 18.6 170.95 Watermelon 3.44 18.6 23.35 Squash/Zucchini 1.26 5.15 2.37 Totals 133.89 2871.78 Total Diet 3071.81 Dose Non-Sampled 2. 18E+00 mrem/yr Sampled 3.73E+00 mrem/yr Total 5.92E+00 mrem/yr 59 conversion factor was also assigned a distribution. The product of these three variables and a conversion factor allowed the determination of a dose and a distribution. Table 6-3 shows the output of the family of analyses obtained when the various distributions were placed into the appropriate variables. Table 6-4 illustrates the statistical data to allow for a comparison of the various distributions. Figure 6-1 is the output of the Crystal Ball forecast for set 9. Figure 6-2 shows the difference comparison between the best fit distribution and the Monte Carlo Crystal Ball determination of the distribution. The scale on the y-axes illustrates that there was close agreement. Table 6-3: Table of Input and Output Distributions for Radium-226 Intake Concentration DCF Dose Set 1 LN LN LN LN Set 2 G LN LN LN Set 3 G G LN LN Set 4 G G G G Set 5 LN G G Beta Set 6 LN LN G Beta Set 7 LN G LN LN Set 8 G LN G Beta Set 9 LN LN LN LN Table 6-4: Statistical Comparison of Various Data for Radium-226 Mean Std Dev Skewness Kurtosis COF Range Width Set 1 5.91 0.623 0.3 3.17 0.11 4.81 Set 2 5.92 0.625 0.32 3.13 0.11 5.16 Set 3 5.92 0.632 0.3 3.15 0.11 5.1 Set 4 5.92 0.629 0.06 3.04 0.11 4.91 Set 5 5.92 0.627 0.05 3.04 0.11 5.12 Set 6 5.92 0.626 0.05 2.97 0.11 4.62 Set 7 5.91 0.624 0.32 3.3 0.11 6.23 Set 8 5.92 0.624 0.08 3.04 0.11 5.28 Set 9 9.56 12.1 5.08 53.59 1.26 270 Overlay Chart Frequency Comparison Icgxrrrd Dstrfaicn l\fen=9S£K) SbDB/=12IEH Tea QOCBO 112&1 22&1 33E&1 43&1 60 Figure 6-1 : Set 9 Output and Distribution Fit for Ra-226 Overlay Chart Frequency Dfference .OB -OB • ■ III ■1 1 1.1 1 1 1 J 1 1 1. . .1 il.l ii, • 1 IT l|. .||.| ii i -■ ■ i| |i |'v.-"."r • • Lcgtjrrd Dstrixticn Mai=95E&0 StlDa/=121&1 TcH QCCBO 112&1 225&1 33E&1 45B-1 Figure 6-2: Difference Chart for Ra-226 Set 9 Lead-210 Analysis on 1990 FIPR Data The lead-210 analyses on the 1990 FIPR data was performed in the same manner as the radium-226 above. The input data, represented in spreadsheet form, is presented in Table 6-5 below. Table 6-6 is the presentation or the distribution data for the various 61 Table 6-5: Input Spreadsheet Data for Lead-210 Dose Calculation (Guidry et al., 1990) DCF 5.40E-03 (mrem/pCi) Diet Item Intake (g/day) Concentration (pCi/kg) Intake (PCi/yr) Broccoli 3.51 60.09 76.98 LEAFY Cabbage 7.04 122.61 315.06 Collard Greens 0.45 33.29 5.47 Lettuce 23.38 75.56 644.81 Mustard Greens 0.45 0.50 0.08 Spinach 3.28 166.49 199.32 Turnip Greens 0.45 40.48 6.65 SEEDS/GRAINS Blackeyed Peas 5.61 22.00 45.05 Rice 22.94 62.26 521.31 Yellow Corn 14.41 22.00 115.71 ROOTS Carrot 2.92 5.97 6.36 Onion 4.19 4.70 7.19 Radish 0.32 4.70 0.55 Turnip 0.42 10.22 1.57 GENERAL Cucumber 2.62 8.00 7.65 Green Beans 8.80 8.00 25.70 Green Peppers 1.99 8.00 5.81 Strawberries 1.23 456.19 204.81 Tomato 25.18 8.00 73.53 Watermelon 3.44 8.00 10.04 Squash/Zucchini 1.26 8.00 3.68 Totals 133.89 2277.31957 Total Diet 3071.81 Dose Non- Sampled 9.07E+00 mrem/yr Sampled 1.23E+01 mrem/yr Total 2.14E+01 mrem/yr 62 Table 6-6: Table of Input and Output Distributions for Lead-210 Intake Concentration DCF Dose Set 1 LN LN LN LN Set 2 G LN LN LN Set 3 G G LN LN Set 4 G G G Beta Set 5 LN G G Beta Set 6 LN LN G G Set 7 LN G LN LN Set 8 G LN G Beta Set 9 LN LN LN LN variables and the final dose. Table 6-7 shows the statistics of interest for the output distributions. Figure 6-3 is shown as the set 9 for this family of distribution analyses. It is believed to be the most probable outcome of dose. Figure 6-4 shows the Crystal Ball output graph of the difference chart. This graph illustrates the difference between the output dose distribution and the closest fit approximation determined by the program and its subsequent Chi-squared test of fit for the curve. Table 6-7: Statistical Comparison of Various Data for Lead-210 Mean Std Dev Skewness Kurtosis COF Range Width Set 1 21.4 2.25 0.32 3.18 0.11 17.6 Set 2 21.4 2.25 0.29 3.1 0.11 18.2 Set 3 21.3 2.25 0.37 3.27 0.11 19.6 Set 4 21.3 2.25 0.06 3.04 0.11 18.4 Set 5 21.4 2.27 0.05 3.06 0.11 19 Set 6 21.3 2.28 0.08 2.99 0.11 19 Set 7 21.4 2.25 0.33 3.18 0.11 18.2 Set 8 21.4 2.28 0.07 3.05 0.11 18.1 Set 9 34.7 43.9 5.18 56.66 1.25 965 63 Overlay Chart Frequency Comparison QCCBO 37»1 73EM nmuBBB 1.12&2 liy tiirrf DstrhJian l\*an=347&1 aJQ*=43£-1 TcB 1.5&2 Figure 6-3: Set 9 Output and Distribution Fit for Pb-210 Overlay Chart Frequency Dfferaxe .OCB-f .GDI .ODD -JDD1 -JDD3 ■ III IJL-sju . 1 . ll .In I.I .1 1. ., ,. . 1 . 1 . . pi 1 | |||| |'|| -I i 1 ■■!■! || II- | ■ -- • •■■ -i ■ i. ■ ■ Lyund Qstrititjcn N*m=345&1 ajQy=43&1 TcH QCC&O 37&1 7.3B-1 1.12&2 13B2 Figure 6-4: Difference Chart for Lead-210 Set 9 Grocery Store Data Analysis Lead-210 The analyses on the grocery store data followed the same approach and methodology as that utilized to perform the analyses on the original FIPR data. Two radionuclides were considered: lead-210 and radium-226. In fact, like the original study, 64 this study counted the foods for two radionuclides: lead-210 and radium-226. The original study provided the data but no analysis on the polonium due to the lack of literature and values for the nonsampled food items and the concentration or dose that could be assigned to these values. A literature search did not turn up enough data to support analysis of this third radionuclide; therefore, similar to the original study, no analyses were performed in relation to it. Each variable is assigned a value. Intake data were obtained from a literature search of previous studies and databases on consumption in the United States. The concentration data for the various foods was obtained by experimental measurement discussed in the fourth chapter. Dose conversion factors were obtained from Federal Regulatory Guide # 1 1. All of these data were provided different distributions to obtain the nine sets of dose distributions and analyses. Table 6-8 shows the input to Crystal Ball. Table 6-9 illustrates the input variable and the output distributions obtained for the various sets tested. Table 6-10 shows the statistical output for the various sets. Figure 6-5 is the forecast output of the Crystal Ball program for the 9 th set, and Figure 6-6 shows the difference between the programs best fit and the output data. Radium-226 Table 6-1 1 illustrates the data input to the program to run the simulation and obtain results. Table 6-12 is the description of the distribution results. Table 6-13 shows the output statistics. Figure 6-7 is the frequency output for set 9, and Figure 6-8 is the difference comparison of this frequency output to the best fit distributions. 65 Table 6-8: Input Spreadsheet Data for Lead-210 Dose Calculation DCF 5.40E-03 (mrem/pCi) Diet Item Intake Concentration (pCi/kg) Intake (pCi/yr) Broccoli 3.51 829 1062.07 LEAFY Cabbage 7.04 858 2204.72 Collard Greens 0.45 1372 225.35 Lettuce 23.38 1237 10556.19 Mustard Greens 0.45 1622 266.41 Spinach 3.28 422 505.22 Turnip Greens 0.45 941 154.56 SEEDS/GRAINS Blackeyed Peas 5.61 494 1011.54 Rice 22.94 654 5476.01 Yellow Corn 14.41 506 2661.38 ROOTS Carrot 2.92 555 591.52 Onion 4.19 599 916.08 Radish 0.32 580 67.74 Turnip 0.42 401 61.47 GENERAL Cucumber 2.62 47082 45024.52 Green Beans 8.80 3837 12324.44 Green Peppers 1.99 431 313.06 Strawberries 1.23 715 321.00 Tomato 25.18 1011 9291.80 Watermelon 3.44 776 974.35 Squash/Zucchini 1.26 613 281.92 Totals 133.89 94291.34 Total Diet 3071.81 Dose Non- Sampled 9.07E+00 mrem/yr Sampled 5.09E+02 mrem/yr Total 5. 18E+02 mrem/yr 66 Table 6-9: Table of Input and Output Distributions for Lead-210 Intake Concentration DCF Dose Set 1 LN LN LN LN Set 2 G LN LN Gamma Set 3 G G LN Gamma Set 4 G G G Gamma Set 5 LN G G Gamma Set 6 LN LN G Gamma Set 7 LN G LN LN Set 8 G LN G Gamma Set 9 LN LN LN LN Table 6-10: Statistical Comparison of Various Dose Rate Results Data for Lead-210 Mean Std Dev Skewness Kurtosis COF Range Width Set 1 518 63.9 0.41 3.26 0.12 563 Set 2 518 64.6 0.36 3.19 0.12 529 Set 3 518 64.2 0.37 3.23 0.12 541 Set 4 518 64.7 0.2 3.08 0.12 588 Set 5 518 63.9 0.21 3.12 0.12 541 Set 6 517 63.8 0.22 3.14 0.12 576 Set 7 518 64.6 0.39 3.26 0.12 529 Set 8 518 63.7 0.21 3.16 0.12 529 Set 9 854 1070 6.02 86.32 1.27 3150 .CB3-T .00 .023 .00 .ODD darby Chart frequency Comparison QCCBO 1.QD&3 20C&3 3.CC&3 Liyund Dstrbioi l\ten=&€&2 SUDb/=1.07&3 TcB 4QC&3 Figure 6-5: Set 9 Output and Distribution Fit for Pb-210 67 Overlay Chart Frequency Dfference COB .GDI .ODD -GDI -COB • :_j J J 1 lJlll.ll.1 .1. 1 - 1 In 1 rrqi ■ 1 1 1 II 1 ' 1 I ' 1 Lnjtmnd Darhijm M3an=84E&2 sbCB/=i.a?&3 Tea QdBO 1.C0B-3 2G0B3 Figure 6-6: Difference Chart for Lead-210 Set 9 Overall Analysis The above sets were each run with 20,000 trials each to decrease statistical error and improve comparability. The data show some very interesting results when compared to each other and then when compared to overall annual dose to an individual. Dose Data Comparison Lead-210 exhibited the highest dose in both the original set of data and the grocery store data. The original FIPR 1990 report data yielded a dose from ingestion of lead 210 of 21.4 mrem/yr for sets 1 through 8 and 34.7 mrem/yr for set 9. The grocery store data yielded a dose to the individual of 518 mrem/yr for sets 1 through 8 and 854 mrem/yr for set 9 individual of 877mrem/yr. The dose calculated from the grocery store data was 24 times higher than that calculated from the 1990 FIPR data. 68 Table 6-11: Input Spreadsheet Data for Radium-226 Dose Calculation (Grocery Data) DCF 1.30E-03 (mrem/pCi) Diet Item Intake Concentration Intake (pCi/yr) Broccoli 3.51 5.00 6.406 LEAFY Cabbage 7.04 6.00 15.418 Collard Greens 0.45 6.00 0.986 Lettuce 23.38 4.00 34.135 Mustard Greens 0.45 17.00 2.792 Spinach 3.28 20.00 23.944 Turnip Greens 0.45 6.00 0.986 SEEDS/GRAINS Blackeyed Peas 5.61 3.00 6.143 Rice 22.94 2.00 16.746 Yellow Corn 14.41 6.00 31.558 ROOTS Carrot 2.92 4.00 4.263 Onion 4.19 4.00 6.117 Radish 0.32 4.00 0.467 Turnip 0.42 1177.00 180.434 GENERAL Cucumber 2.62 9.00 8.607 Green Beans 8.80 7.00 22.484 Green Peppers 1.99 4.00 2.905 Strawberries 1.23 4.00 1.796 Tomato 25.18 3.00 27.572 Watermelon 3.44 2.00 2.511 Squash/Zucchini 1.26 4.00 1.840 Totals 133.89 398.109 Total Diet 3071.81 Dose Non-Sampled 2.18E+00mrem/yr Sampled 5.18E-01 mrem/yr Total 2.70E+00 m/rem/yr 69 Table 6-12: Table of Input and Output Distributions for Radium-226 (Grocery Data) Intake Concentration DCF Dose Set 1 LN LN LN LN Set 2 G LN LN Gamma Set 3 G G LN Gamma Set 4 G G G Beta Set 5 LN G G Beta Set 6 LN LN G Beta Set 7 LN G LN Gamma Set 8 G LN G Beta Set 9 LN LN LN LN Table 6-13: Statistical Comparison (Grocery Data) Df Various Dose Rate Results Data for Radium-226 Mean Std Dev Skewness Kurtosis COF Range Width Set 1 2.7 0.273 0.31 3.22 0.1 2.27 Set 2 2.7 0.275 0.31 3.29 0.1 2.25 Set 3 2.7 0.274 0.31 3.15 0.1 2.06 Set 4 2.7 0.27 0.02 2.95 0.1 2.1 Set 5 2.7 0.273 2.95 0.1 2.21 Set 6 2.7 0.272 0.04 3.03 0.1 2.16 Set 7 2.7 0.271 0.3 3.21 0.1 2.45 Set 8 2.7 0.272 -0.01 3.02 0.1 2.09 Set 9 4.38 5.52 5.6 69.91 1.28 150 .08 1 Overlay Chart Freqjency Comparison Ixgrnrrd DstrfcUicn Wten=43EB0 SHQy=55»0 TcB QCC&O 5CEB0 1.GC&1 1.SD-1 2CC&1 Figure 6-7: Set 9 Output and Distribution Fit for Radium-226 (Grocery Data) ODB -OB n Overlay Chart Frequency Dfferenoe 'i " i JiWi ' h i ■ ^ ■ ' -■■ ' ■ - ■■ ■ ■ v- - ■' „ Tmrn I ■ (HBO 50BO IxgncirrEi Dsfirbiicn ltei=43E&0 SaQy=55£K) Tea ia&i 1.3E-1 20CB-1 Figure 6-8: Difference Chart for Radium-226 Set 9 (Grocery Data) 70 The dose from the grocery store data is believed to be higher for two reasons. The peak measured on the original analysis was the 40 KeV peak. The peak measured on the grocery store analysis was the 10.8 KeV peak. This peak was measured because of the successful recognition of this peak by the GammaVision program for this peak for the lead-210 radionuclide. This 10.8 KeV peak yielded a significantly higher correction factor than previously measured and observed for the alternate lead-210 peak. Radium-226 had the lowest dose per year of both radionuclides considered. The output from the analysis of the 1990 FIPR data yielded a dose to the individual from radium-226 of 5.91 mrem/yr for sets 1 through 8 and 9.56 for set 9. The grocery store data provided an individual dose that was lower than the FIPR data. The grocery store data dose to the individual was calculated to be 2.7 mrem/yr for sets 1-8 and 4.38 for set 9. The dose calculated from the grocery store data was 45% of the dose calculated for the original FIPR dose calculation. 71 Comparing the dose to the individual from radium-226 and lead-2 1 from the FIPR data, it was calculated that dose from lead-2 10 was 3.6 times higher than the individuals dose from radium-226. A similar comparison of doses for the grocery store data concluded that the individual's dose attributable to lead-210 was 191 times greater than that attributable to radium-226 Some of the differences between doses attributable to the radionuclides can be traced back to their reported dose conversion factors. Lead-210 is almost three times larger than radium-226. Consider this factor with the fact that lead-210 had some individual samples with high counts and a higher intersample comparison should be expected. Comparison of Distributions and Statistics The dose conversion factor distribution appears to have a strong effect on the dose distribution. A sensitivity analysis was performed on the various variables with the outcome determining that the dose conversion factor was over 10 times more sensitive to the output distribution that any other variable. The data reveal that multiplying three lognormal distribution yields a lognormal output distribution each time. Multiplying three normal distributions times each other provides a normal distribution for the output dose in two cases and a beta distribution in two other cases. Multiplying a mixture of lognormal distributions and normal distributions does not necessarily yield either of these distributions as an output. The best fit to the dose distribution output in the preceding case is illustrated above to be a lognormal, a normal, a beta, or a gamma distribution. 72 The beta distribution is a very flexible distribution commonly utilized to represent variability over a wide range (Decisioneering, 1996). This distribution can assume a wide variety of shapes when the values of alpha a beta are varied. The gamma distribution is related to the lognormal distribution and is used sometimes to represent pollutant concentrations and precipitation quantities. Set 9, in all four sets of analyses, was utilized to represent the most accurate quantity. The value of this dose in all four groups was significantly higher that the other eight sets in that group under consideration. The primary reason for this is the change in the dose conversion factor. Being the most sensitive variable and the large skewness introduced due to the determination of an accurate shape of this curve from a discussion with Dr. Eckerman, this provided an output dose distribution different from the other sets. Conclusions The purpose of this chapter was accomplished by a literature search that described the applicable and relevant literature to determine the committed effective dose equivalent, the term to describe the extended dose to an individual based on intake of a specific radionuclide. The data previously obtained were then analyzed with the original data and a comparison is provided. The shape of various dose distributions to individuals was determined for nine combinations of variable distributions in each of the two radionuclides in each of the two studies. The data from one study came from a previous 1990 FIPR report. The data for the other study were determined by experimental measurement from an earlier chapter in this series. The Crystal Ball program and monte carlo sampling method inherent to it were utilized to perform these analyses for each set of distributions. 73 The average individual annual dose, as stated in the introduction, is 360 mrem/yr. Lead-210 measurement is 518 mrem/yr for eight sets of analyses on grocery store samples and 854 mrem/yr for the most likely distribution scenario. The lead-210 dose to an individual from the analysis of the FIPR data was 34.7 mrem/yr for the case 9 and 21 .4 mrem/yr for all others. The case 9 set of variable distributions is believed to be the most likely dose output. This output distribution is described by a lognormal distribution. Many reasons were observed for the higher value from the experimental data dose determination. A different peak measurement and a higher correction factor were both significant factors as well as the fact that the 10.8 KeV is at the lower edge of analysis for the system. In defense of a higher lead-210 dose, the original 1990 FIPR report chose not to use grocery store data due to the fact that only single replicates were being measured and the alternate fact that the dose obtained was 200 times greater than the other measurements. The radium-226 individual dose measurements for the case 9, the most likely case, also followed a lognormal distribution. The values of the dose to the individual were significantly lower than the lead-210 values. The dose for the FIPR data was 5.91 mrem/yr for eight cases and 9.56 mrem/yr for the ninth and most likely case. The grocery store data provided a dose to the individual that measured 2.7 mrem/yr for 8 sets and 4.38 mrem/yr for the most likely case. These data, compared to the 360 mrem/yr expected dose from natural sources, are less than 3% for all radium-226 measurements. The distributions described by the various analyses included normal, lognormal, beta, and gamma. The output, dose, and distributions were strongly influenced by the distribution assigned to the dose conversion factor variable. 74 This chapter is designed to determine a probabilistic dose to individuals from foods bought at local stores in Gainesville, Florida. The first chapter provided the introduction of a probabilistic dose approach. The second chapter described the literature search for the overall dissertation to determine the references that were used for each section. The third chapter determined the dietary intake values to be used and the most probable distribution to describe them. The fourth chapter described the actual experimentation performed to determine both the concentration of specific radionuclides in the various foods measured and the distribution to describe this concentration. The fifth chapter described the methodology to determine the dose conversion factor (DCF) value and distribution. The purpose of this chapter was to determine the value and distribution to describe the dose to an individual based on the values obtained in the previous chapters. The next and final chapter provides a conclusion and recommendations for future research in this area. CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS This is the seventh and the last chapter intended to design and implement a methodology to determine a probabilistic radiation dose to individuals. This methodology is analyzed by application to data experimentally determined from foods bought at local stores in Gainesville, Florida. The first chapter in the series provided the introduction of a probabilistic dose approach. The explanation of how the current approach to individual dose determination was deterministic and resulted in a dose with a single number describing it. A probabilistic approach was explained and how this yielded a dose that was described with a distribution. The second chapter described the literature search for the overall dissertation to determine the references that were used for each section. This general literature search provided the basis for the background data utilized for the remainder of the dissertation. The third chapter determined the dietary intake values to be used and the most probable distribution to describe them. These values and data were derived from literary sources of previous studies and dietary surveys performed in the United States. The fourth chapter described the actual experimentation performed to determine both the concentration of specific radionuclides in the various foods measured and the distribution to describe this concentration. Samples from three different local stores were analyzed to determine concentrations of radium-226 and lead-210 in the foods. An 75 76 additional study was performed to determine experimentally the type of distribution to describe best the concentration in foods. The fifth chapter described the methodology to determine the dose conversion factor (DCF) value and distribution. Literary sources as well as direct conversation with people at the cutting edge of dose conversion factor determination provided the data obtained in this chapter for the value and distributions to describe the dose conversion factor. The sixth chapter determined the value and distribution to describe the dose to an individual based on the values obtained in the previous chapters. The Crystal Ball program was utilized to perform groups of analyses on both original 1990 Florida Institute of Phosphate Research data as well as grocery store data. Crystal Ball is like any computer program. Good information in will yield good information out. The data that were measured had numerous data points that provided no counts at the specific peaks that were being observed. Minimum detectable activity numbers were input for these data points to provide for a large and, therefore conservative from a safety standpoint, dose estimate. The unsampled data points provided another source of error which was overcome by reference to previous work and data manipulation to provide a dose for these data points. This, however, provides another possible source for higher dose output. The Crystal Ball program provided an accurate way to sample the input to provide a distribution output that was as accurate as the input provided. The grocery store data showed a lognormal distribution for lead-210 with an average dose 854 mrem/yr for the most probable case and 518 mrem/yr for all other eight 77 cases. The FIPR data illustrated a lead-210 mean of 34.7 mrem/yr for the most probable case and 21 .4 consistently for all other cases. The reasons for such a high lead-210 dose is due to many factors: different peak counted, different calibration or correction factor, and the peak measured being at the lower edge of the detector's measurement limit. This number, as stated before, seems abnormally high and should be verified with other analyses. The grocery store radium-226 measurement for individual dose, by comparison, was 2.7 mrem/yr for eight cases and 4.38 mrem/yr for the ninth and most probable case. This value was lower than the individual dose value obtained from the data from the 1990 FIPR report. This report yielded an individual dose of 5.91 mrem/yr for eight cases and 9.56 mrem/yr for the most probable case. The most probable dose scenarios followed a lognormal distribution that closely approximated the dose conversion factor input distribution. The numbers for radium-226 are very similar to those obtained by FIPR in the 1990 report and so support their data as well as extending the database. The lead-210 measured in this report are consistent with the previous report in the fact that the lead-210 general foods category radiation dose calculation from the grocery store samples ranged from 2 to 200 times higher than the literature value (Guidry et al., 1990). The methodology of using Crystal Ball and probabilistic dose calculation was successfully implemented in the previous chapter. The inclusion of distributions to account for fluctuations, errors and variations was very useful and provided a higher initial dose than the deterministic approach in the previous FIPR paper (Guidry et al., 1990). The distribution groups allow for flexibility should future research determine more 78 accurate distributions for the variables. Additionally, the output distributions provide a visual aid for the public and researchers to understand radiation dose and the fact that it is a range and not just one number! Future analyses should, if possible, include the location of where samples are grown. Additional measurements should be taken to determine and confirm the normal distribution assigned to the food concentration. Additional Crystal Ball analysis should be performed on the calculational parameters and, therefore, the solution for the dose conversion factor formula. This would provide a more accurate distribution for the dose per unit intake factor. An analysis to determine the differences and advantages of the various dose conversion factors should be considered. A study should also be undertaken to determine the effect on changing the various distributions on the final dose. A determination should be made as to what may be the cause for the elevated measurements for lead-210. These are a few suggestions on the direction that this work should take in the future. APPENDIX A DATA SHEETS Item Store Weight Time Counted Detector File Saved Beef Publix 556.6 34187.1 4 beef.spc Beef Kidney Publix 449.2 86362.4 4 bfkid.spc Black-Eyed Peas Publix 455.35 86437.5 2 bleypeas Black-Eyed Peas Albertsons 264.3 72000 2 bepe.spc Black-Eyed Peas Winn Dixie 473.8 34098.9 4 bley3.spc Brazil Shells Publix 304.2 43149 2 bznutssh.spc Broccoli Publix 267 34167.9 4 brocclspc Broccoli Albertsons 192.4 71946.1 2 broc2.spc Broccoli Winn Dixie 324.4 34124.9 2 broc3.spc Cabbage Publix 210.45 34187.4 2 cabb.spc Cabbage Albertsons 179.3 34155.1 4 cabb2.spc Cabbage Winn Dixie 214.15 34122.6 4 cabb3.spc Carrots Publix 286.9 34187.8 2 carr.spc Carrots Albertsons 421.1 71940.8 4 carr2.spc Carrots Wnn Dixie 365.9 34061.3 4 carr3.spc Cauliflower Publix 268.8 34187.4 4 caul.spc Cauliflower Albertsons 154.45 34187.5 2 caul2.spc Cauliflower Winn Dixie 396.1 34167.7 2 caul3.spc Collard Greens Publix 140.35 34187.9 4 cogr.spc Collard Greens Albertsons 421.15 71940.8 2 cogr2.spc Collard Greens Wnn Dixie 136.6 34104.7 2 cogr3.spc Com Publix 289.85 34194.1 2 corn.spc Corn Albertsons 199.6 34187.3 4 corn2.spc Corn Wnn Dixie 418.4 34051.1 4 corn3.spc Cucumber Publix 347.55 34167.9 2 cuculspc Cucumber Albertsons 257.6 71942.7 2 cucu2.spc Cucumber Wnn Dixie 324.2 34087.2 2 cucu3.spc Eggplant Publix 238.4 34187.8 2 eggp.spc Eggplant Albertsons 231.7 71970.2 4 egpl2.spc Eggplant Wnn Dixie 130.3 34089 2 eggp3.spc Grapefruit Publix 448.1 34186.8 4 grap.spc Grapefruit Albertsons 317.6 71944 4 grap2.spc Grapefruit Wnn Dixie 422.5 34089 4 grap3.spc 80 81 Item Store Weight Time Counted Detector File Saved Green Beans Publix 216.7 34186.9 4 grbr.spc Green Beans Albertsons 250 71971.9 2 grbe2.spc Green Beans Winn Dixie 338 34036.9 2 grbe3.spc Green Onions Publix 97.2 34187.8 4 gron.spc Green Onions Albertsons 89.1 71972.1 4 gron2.spc Green Onions Winn Dixie 195.15 34100.7 2 gron3.spc Green Peppers Publix 321 34186.9 2 grpe.spc Green Peppers Albertsons 287.5 71941.8 4 grpe2.spc Green Peppers Winn Dixie 415.75 34097.7 4 grpe3.spc Irish Creamer Potatoes Publix 353.75 34186 4 icp.spc Lemons Publix 316.9 43176.9 4 lem.spc Lemons Albertsons 238.75 71941.8 2 lemo2.spc Lemons Wnn Dixie 372.7 34154.8 4 lemo3.spc Lettuce Publix 218.8 43181.5 2 lettw.spc Lettuce Albertsons 201.1 71944 2 Iett2.spc Lettuce Wnn Dixie 319.45 34099.5 2 Iett3.spc Lima Beans Publix 362.7 43182.2 2 lima.spc Lima Beans Albertsons 358.65 71942.7 4 Iibe2.spc Lima Beans Wnn Dixie 382.6 34040.6 2 Iibe3.spc Mustard Greens Albertsons 81.35 34187.5 4 mugr.spc Okra Publix 180.5 34186 2 okra.spc Okra Albertsons 240.5 71970.2 2 okra2.spc Okra Wnn Dixie 320.3 34167.4 4 okra4.spc Onions Publix 335.6 43181.9 2 onio.spc Onions Albertsons 323.15 71979.8 2 onio2.spc Onions Wnn Dixie 332.1 34037.1 4 onio3.spc Oranges Publix 446.9 43176.9 2 oran.spc Oranges Albertsons 381.3 71973.3 2 oran2.spc Oranges Wnn Dixie 379.6 34030.4 4 oran3.spc Parsley Publix 71.25 43179.7 4 pars.spc Parsley Albertsons 17.8 34181 2 pars2.spc Parsley Wnn Dixie 175.75 34062 2 pars3.spc 82 Item Store Weight Time Counted Detector File Saved Peas Publix 263.2 43180.5 2 peas.spc Peas Albertsons 289.35 71970.9 4 peas2.spc Peas Winn Dixie 342.6 33922.1 2 peas3.spc Pole Beans Publix 267.15 34186.8 2 pb.spc Pole Beans Winn Dixie 416.5 34057.6 4 pobe3.spc Potato Publix 398 43179.7 2 pot.spc Potato Albertsons 254.45 86366.8 2 pot2.spc Potato Winn Dixie 390.3 34154.9 2 pot3.spc Purple Hull Peas Publix 391.05 43182.3 4 php.spc Purple Hull Peas Winn Dixie 430.3 34200 2 crpe3.spc Radishes Publix 333.7 34128.8 4 rad.spc Radishes Albertsons 170.1 71968.7 4 radi2.spc Radishes Winn Dixie 310.3 34100.9 4 rad3.spc Red Potatoes Publix 348.15 43182.2 4 rpotspc Red Potatoes Winn Dixie 371.8 34086.4 4 rpot3.spc Rice Publix 518.55 43182 4 rc.spc Rice Albertsons 446.8 71968.6 2 rice2.spc Rice Winn Dixie 583.85 34078.7 2 rice3.spc Spinach Publix 99.85 34185.9 4 sp.spc Spinach Albertsons 69.3 22702.8 4 spin2.spc Spinach Winn Dixie 484.7 34077.8 4 spin3.spc Strawberries Publix 348.75 34126.7 2 stra.spc Strawberries Albertsons 278.5 71973.3 4 straw2.spc Strawberries Winn Dixie 337.1 34051.8 2 straw3.spc Swiss Chard Publix 173.65 34187.1 2 swch.spc Tangerine Albertsons 276 34155.2 2 tan2.spc Tangerine Winn Dixie 399.85 34109.5 4 tan3.spc Tomatoes Publix 358.8 43181.4 4 tomat.spc Tomatoes Albertsons 376.05 34191.8 2 tom2w.spc Tomatoes Wnn Dixie 434.4 34048 2 5om3.spc Turnip Greens Publix 135.65 43183.1 4 tg.spc Turnip Greens Albertsons 313.65 34181.8 4 tugr2.spc Turnip Greens Winn Dixie 564.2 34185.4 2 tugr3.spc 83 Item Store Weight Time Counted Detector File Saved Turnip Root and Green Publix 189.65 34186 2 trag.spc Turnip Roots Publix 275.1 43148.7 4 turnroots.spc Turnip Roots Albertsons 0.3 71972.2 2 tum2.spc Watermelon Publix 463.6 43182.4 2 wm.spc Watermelon Albertsons 396 34187.4 2 wat2.spc Yellow Corn Publix 324.6 43182.1 2 yc.spc Yellow Corn Albertsons 234.75 34191.7 4 yc2.spc Yellow Corn Winn Dixie 386.6 34167.8 2 yeco3.spc Yellow Squash Publix 331.6 43183.1 2 yesq.spc Yellow Squash Albertsons 219.4 86366.8 4 yesq2.spc Yellow Squash Winn Dixie 361.9 33914.5 4 yellow3.spc Zucchini Publix 394.3 43180.5 4 zucc.spc Zucchini Albertsons 256.4 71971.9 4 zucc2.spc Zucchini Winn Dixie 368.7 34167.8 4 zucc3.spc Brazil Nuts 226 86369 4 bznuts.spc 84 Pb-210 Peaks Pb-210 10.8 KeV Item Net (Counts) Error Beef Beef Kidney 126 47 Black-Eyed Peas Black-Eyed Peas Black-Eyed Peas Brazil Shells Broccoli Broccoli Broccoli Cabbage Cabbage Cabbage 45 12 Carrots Carrots 91 45 Carrots Cauliflower 105 27 Cauliflower Cauliflower Collard Greens 43 26 Collard Greens Collard Greens Corn Corn Corn Cucumber 4779 142 Cucumber 182 35 Cucumber Eggplant Eggplant Eggplant Grapefruit Grapefruit Grapefruit 85 Pb-210 Peaks Pb-210 10.8 KeV Item Net (Counts) Error Green Beans 437 59 Green Beans 211 37 Green Beans Green Onions Green Onions Green Onions Green Peppers Green Peppers Green Peppers Irish Creamer Potatoes Lemons Lemons Lemons Lettuce Lettuce Lettuce Lima Beans 76 Lima Beans 76 47 Lima Beans Mustard Greens 41 29 Okra Okra Okra 28 8 Onions Onions Onions Oranges Oranges 100 38 Oranges Parsley Parsley Parsley 86 Pb-210 Peaks Pb-210 10.8 KeV Item Net (Counts) Error Peas Peas 49 44 Peas Pole Beans Pole Beans Potato Potato Potato Purple Hull Peas Purple Hull Peas Radishes 19 30 Radishes 143 43 Radishes 26 7 Red Potatoes Red Potatoes 37 12 Rice Rice 122 39 Rice Spinach Spinach Spinach Strawberries Strawberries Strawberries Swiss Chard Tangerine Tangerine Tomatoes Tomatoes Tomatoes 87 18 Turnip Greens 69 33 Turnip Greens Turnip Greens 79 20 87 Pb-210 Peaks Pb-210 10.8 KeV Item Net (Counts) Error Turnip Root and Green Turnip Roots 53 33 Turnip Roots Watermelon Watermelon Yellow Corn Yellow Corn Yellow Corn Yellow Squash Yellow Squash 135 44 Yellow Squash Zucchini Zucchini Zucchini Brazil Nuts 235 86 88 Ra-226 Peaks Pb-214 295 KeV Pb-214 352 KeV Bi-214 609 KeV Item Net (Counts) Error Net (Counts) Error Net (Counts) Error Beef Beef Kidney 271 30 Black-Eyed Peas Black-Eyed Peas Black-Eyed Peas Brazil Shells 495 42 904 43 541 31 Broccoli Broccoli Broccoli 39 32 69 29 Cabbage Cabbage 96 32 248 30 233 22 Cabbage 82 29 Carrots Carrots 140 44 181 42 Carrots 95 20 Cauliflower Cauliflower Cauliflower Collard Greens 81 25 Collard Greens Collard Greens Corn Corn Corn Cucumber Cucumber 51 31 Cucumber Eggplant Eggplant 75 44 271 37 237 28 Eggplant Grapefruit Grapefruit 150 39 Grapefruit 102 26 80 23 89 Ra-226 Peaks Pb-214 295 KeV Pb-214 352 KeV Bi-214 609 KeV Item Net (Counts) Error Net (Counts) Error Net (Counts) Error Green Beans Green Beans Green Beans Green Onions Green Onions 227 38 Green Onions Green Peppers Green Peppers 387 411 303 30 Green Peppers Irish Creamer Potatoes 37 Lemons 67 27 Lemons Lemons 6 7 Lettuce Lettuce Lettuce o - Lima Beans 299 Lima Beans 180 43 299 40 Lima Beans Mustard Greens 189 26 Okra Okra Okra Onions Onions Onions Oranges Oranges Oranges Parsley 100 29 Parsley Parsley 90 Ra-226 Peaks Pb-214 295 KeV Pb-214 352 KeV Bi-214 609 KeV Item Net (Counts) Error Net (Counts) Error Net (Counts) Error Peas Peas 163 38 Peas Pole Beans Pole Beans 75 24 Potato Potato Potato Purple Hull Peas 66 33 Purple Hull Peas Radishes Radishes 203 37 187 27 Radishes Red Potatoes Red Potatoes Rice Rice Rice Spinach Spinach Spinach Strawberries Strawberries 242 25 Strawberries Swiss Chard Tangerine Tangerine 114 15 Tomatoes 100 20 Tomatoes Tomatoes Turnip Greens 156 29 104 18 Turnip Greens Turnip Greens 91 Ra-226 Peaks Pb-214 295 KeV Pb-214 352 KeV Bi-214 609 KeV Item Net (Counts) Error Net (Counts) Error Net (Counts) Error Turnip Root and Green Turnip Roots 63 33 Turnip Roots Watermelon Watermelon Yellow Corn Yellow Corn 159 29 126 120 Yellow Com Yellow Squash Yellow Squash 145 40 183 29 Yellow Squash 35 24 Zucchini 32 30 Zucchini Zucchini Brazil Nuts 4586 167 6936 105 4998 83 92 Calibration Factors Bkgnd Count Minimum Det. Activity Pb-210 Ra-226 Pb-210 Ra-226 Pb-210 Ra-226 Item (pCi/cps) (pCi/cps) (counts) (counts) (pCi/g) (PCi/g) Beef 1.10E+05 1664 0.000637 0.0062 7.63E-02 3.60E-03 Beef Kidney 1.10E+05 1664 0.000637 0.0062 5.95E-02 2.81 E-03 Black-Eyed Peas 3.40E+05 1670 0.0045 0.0016 4.82E-01 1.41E-03 Black-Eyed Peas 3.40E+05 1670 0.0045 0.0016 9.10E-01 2.67E-03 Black-Eyed Peas 1.10E+05 1664 0.000637 0.0062 8.98E-02 4.24E-03 Brazil Shells 3.40E+05 1670 0.0045 0.0016 1 .02E+00 2.99E-03 Broccoli 1.10E+05 1664 0.000637 0.0062 1.59E-01 7.51 E-03 Broccoli 3.40E+05 1670 0.0045 0.0016 1 .25E+00 3.66E-03 Broccoli 3.40E+05 1670 0.0045 0.0016 1.08E+00 3.15E-03 Cabbage 3.40E+05 1670 0.0045 0.0016 1.66E+00 4.86E-03 Cabbage 1.10E+05 1664 0.000637 0.0062 2.37E-01 1.12E-02 Cabbage 1.10E+05 1664 0.000637 0.0062 1.99E-01 9.37E-03 Carrots 3.40E+05 1670 0.0045 0.0016 1.22E+00 3.56E-03 Carrots 1.10E+05 1664 0.000637 0.0062 6.96E-02 3.28E-03 Carrots 1.10E+05 1664 0.000637 0.0062 1.16E-01 5.49E-03 Cauliflower 1.10E+05 1664 0.000637 0.0062 1.58E-01 7.46E-03 Cauliflower 3.40E+05 1670 0.0045 0.0016 2.26E+00 6.62E-03 Cauliflower 3.40E+05 1670 0.0045 0.0016 8.82E-01 2.58E-03 Collard Greens 1.10E+05 1664 0.000637 0.0062 3.03E-01 1.43E-02 Collard Greens 3.40E+05 1670 0.0045 0.0016 5.71 E-01 1.67E-03 Collard Greens 3.40E+05 1670 0.0045 0.0016 2.56E+00 7.49E-03 Corn 3.40E+05 1670 0.0045 0.0016 1 .20E+00 3.53E-03 Corn 1.10E+05 1664 0.000637 0.0062 2.13E-01 1.00E-02 Corn 1.10E+05 1664 0.000637 0.0062 1.02E-01 4.80E-03 Cucumber 3.40E+05 1670 0.0045 0.0016 1.00E+00 2.94E-03 Cucumber 3.40E+05 1670 0.0045 0.0016 9.34E-01 2.74E-03 Cucumber 3.40E+05 1670 0.0045 0.0016 1.08E+00 3.16E-03 Eggplant 3.40E+05 1670 0.0045 0.0016 1.46E+00 4.29E-03 Eggplant 1.10E+05 1664 0.000637 0.0062 1.26E-01 5.97E-03 Eggplant 3.40E+05 1670 0.0045 0.0016 2.68E+00 7.86E-03 Grapefruit 1.10E+05 1664 0.000637 0.0062 9.48E-02 4.48E-03 Grapefruit 1.10E+05 1664 0.000637 0.0062 9.22E-02 4.35E-03 Grapefruit 1.10E+05 1664 0.000637 0.0062 1.01 E-01 4.75E-03 93 Item Green Beans Green Beans Green Beans Green Onions Green Onions Green Onions Green Peppers Green Peppers Calibration Factors Pb-210 (pCi/cps) (pCi/cps) Green Peppers 1.10E+05 3.40E+05 3.40E+05 1.10E+05 1.10E+05 3.40E+05 3.40E+05 1.10E+05 Ra-226 1664 1670 1670 1664 1664 1670 1670 1664 1.10E+05 1664 Bkgnd Count Pb-210 (counts) Ra-226 (counts) 0.000637 0.0045 0.0045 0.000637 0.000637 0.0045 0.0045 0.000637 0.000637 0.0062 0.0016 0.0016 0.0062 0.0062 0.0016 0.0062 Minimum Pet. Activity Pb-210 (pcj'g) 1.96E-01 9.62E-01 1.04E+00 4.37E-01 3.29E-01 1.79E+00 0.0016 1.09E+00 0.0062 1.02E-01 1.02E-01 Ra-226 (pCi/g) 9.25E-03 2.82E-03 3.03E-03 2.06E-02 1.55E-02 5.25E-03 3.19E-03 4.81 E-03 4.83E-03 Irish Creamer Potatoes 1.10E+05 1664 0.000637 0.0062 1.20E-01 5.67E-03 Lemons 1.10E+05 1664 0.000637 0.0062 1.19E-01 5.63E-03 Lemons 3.40E+05 1670 0.0045 0.0016 1.01E+00 2.95E-03 Lemons 1.10E+05 1664 0.000637 0.0062 1.14E-01 5.38E-03 Lettuce 3.40E+05 1670 0.0045 0.0016 1 .42E+00 4.16E-03 Lettuce 3.40E+05 1670 0.0045 0.0016 1.20E+00 3.50E-03 Lettuce 3.40E+05 1670 0.0045 0.0016 1 .09E+00 3.20E-03 Lima Beans 3.40E+05 1670 0.0045 0.0016 8.56E-01 2.51 E-03 Lima Beans 1.10E+05 1664 0.000637 0.0062 8.17E-02 3.85E-03 Lima Beans 3.40E+05 1670 0.0045 0.0016 9.14E-01 2.68E-03 Mustard Greens 1.10E+05 1664 0.000637 0.0062 5.22E-01 2.47E-02 Okra 3.40E+05 1670 0.0045 0.0016 1 .93E+00 5.66E-03 Okra 3.40E+05 1670 0.0045 0.0016 1.00E+00 2.93E-03 Okra 1.10E+05 1664 0.000637 0.0062 1.33E-01 6.26E-03 Onions 3.40E+05 1670 0.0045 0.0016 9.26E-01 2.71 E-03 Onions 3.40E+05 1670 0.0045 0.0016 7.44E-01 2.18E-03 Onions 1.10E+05 1664 0.000637 0.0062 1.28E-01 6.05E-03 Oranges 3.40E+05 1670 0.0045 0.0016 6.95E-01 2.04E-03 Oranges 3.40E+05 1670 0.0045 0.0016 6.31 E-01 1.85E-03 Oranges 1.10E+05 1664 0.000637 0.0062 1.12E-01 5.30E-03 Parsley 1.10E+05 1664 0.000637 0.0062 5.31 E-01 2.50E-02 Parsley 3.40E+05 1670 0.0045 0.0016 1.96E+01 5.74E-02 Parsley 3.40E+05 1670 0.0045 0.0016 1.99E+00 5.83E-03 94 Calibration Factors Bkgnd Count Minimum Det. Activity Pb-210 Ra-226 Pb-210 Ra-226 Pb-210 Ra-226 Item (pCi/cps) (pCi/cps) (counts) (counts) (pCi/g) (PCi/g) Peas 3.40E+05 1670 0.0045 0.0016 1.18E+00 3.46E-03 Peas 1.10E+05 1664 0.000637 0.0062 1.01E-01 4.78E-03 Peas 3.40E+05 1670 0.0045 0.0016 1.02E+00 3.00E-03 Pole Beans 3.40E+05 1670 0.0045 0.0016 1.31E+00 3.83E-03 Pole Beans 1.10E+05 1664 0.000637 0.0062 1 .02E-01 4.82E-03 Potato 3.40E+05 1670 0.0045 0.0016 7.80E-01 2.29E-03 Potato 3.40E+05 1670 0.0045 0.0016 8.63E-01 2.53E-03 Potato 3.40E+05 1670 0.0045 0.0016 8.95E-01 2.62E-03 Purple Hull Peas 1.10E+05 1664 0.000637 0.0062 9.67E-02 4.56E-03 Purple Hull Peas 3.40E+05 1670 0.0045 0.0016 8.11E-01 2.38E-03 Radishes 1.10E+05 1664 0.000637 0.0062 1.27E-01 6.01 E-03 Radishes 1.10E+05 1664 0.000637 0.0062 1.72E-01 8.13E-03 Radishes 1.10E+05 1664 0.000637 0.0062 1.37E-01 6.47E-03 Red Potatoes 1.10E+05 1664 0.000637 0.0062 1 .09E-01 5.13E-03 Red Potatoes 1.10E+05 1664 0.000637 0.0062 1.14E-01 5.40E-03 Rice 1.10E+05 1664 0.000637 0.0062 7.29E-02 3.44E-03 Rice 3.40E+05 1670 0.0045 0.0016 5.39E-01 1 58E-03 Rice 3.40E+05 1670 0.0045 0.0016 5.99E-01 1.75E-03 Spinach 1.10E+05 1664 0.000637 0.0062 4.26E-01 2.01 E-02 Spinach 1.10E+05 1664 0.000637 0.0062 7.52E-01 3.55E-02 Spinach 1.10E+05 1664 0.000637 0.0062 8.78E-02 4.14E-03 Strawberries 3.40E+05 1670 0.0045 0.0016 1.00E+00 2.93E-03 Strawberries 1.10E+05 1664 0.000637 0.0062 1 .05E-01 4.96E-03 Strawberries 3.40E+05 1670 0.0045 0.0016 1.04E+00 3.04E-03 Swiss Chard 3.40E+05 1670 0.0045 0.0016 2.01 E+00 5.89E-03 Tangerine 3.40E+05 1670 0.0045 0.0016 1.27E+00 3.71 E-03 Tangerine 1.10E+05 1664 0.000637 0.0062 1 .06E-01 5.02E-03 Tomatoes 1.10E+05 1664 0.000637 0.0062 1.05E-01 4.97E-03 Tomatoes 3.40E+05 1670 0.0045 0.0016 9.28E-01 2.72E-03 Tomatoes 3.40E+05 1670 0.0045 0.0016 8.05E-01 2.36E-03 Turnip Greens 1.10E+05 1664 0.000637 0.0062 2.79E-01 1.32E-02 Turnip Greens 1.10E+05 1664 0.000637 0.0062 1 .35E-01 6.39E-03 Turnip Greens 3.40E+05 1670 0.0045 0.0016 6.19E-01 1.81 E-03 95 Calibration Factors Bkgnd Count Minimum Det. Activity Pb-210 Ra-226 Pb-210 Ra-226 Pb-210 Ra-226 Item (pCi/cps) (pCi/cps) (counts) (counts) (pCi/g) (PCi/g) Turnip Root and Green 3.40E+05 1670 0.0045 0.0016 1.84E+00 5.39E-03 Turnip Roots 1.10E+05 1664 0.000637 0.0062 1.37E-01 6.49E-03 Turnip Roots 3.40E+05 1670 0.0045 0.0016 8.02E+02 2.35E+00 Watermelon 3.40E+05 1670 0.0045 0.0016 6.70E-01 1.96E-03 Watermelon 3.40E+05 1670 0.0045 0.0016 8.82E-01 2.58E-03 Yellow Corn 3.40E+05 1670 0.0045 0.0016 9.57E-01 2.80E-03 Yellow Corn 1.10E+05 1664 0.000637 0.0062 1.81E-01 8.54E-03 Yellow Corn 3.40E+05 1670 0.0045 0.0016 9.03E-01 2.65E-03 Yellow Squash 3.40E+05 1670 0.0045 0.0016 9.37E-01 2.74E-03 Yellow Squash 1.10E+05 1664 0.000637 0.0062 1.22E-01 5.75E-03 Yellow Squash 1.10E+05 1664 0.000637 0.0062 1.18E-01 5.56E-03 Zucchini 1.10E+05 1664 0.000637 0.0062 9.59E-02 4.53E-03 Zucchini 1.10E+05 1664 0.000637 0.0062 1.14E-01 5.39E-03 Zucchini 1.10E+05 1664 0.000637 0.0062 1.15E-01 5.44E-03 Brazil Nuts 1.10E+05 1664 0.000637 0.0062 1.18E-01 5.58E-03 96 Actual Reported Averages Pb-210 Ra-226 Pb-210 Ra-226 Pb-210 Ra-226 Item (pCi/g) (PCi/g) (PCi/g) (PCi/g) (PCi/g) (PCi/g) Beef 0.00E+00 O.OOE+00 0.076 0.004 0.076 0.004 Beef Kidney 3.57E-01 2.02E-03 0.357 0.002 0.357 0.002 Black-Eyed Peas 0.000 0.000 0.482 0.001 0.494 0.003 Black-Eyed Peas 0.000 0.000 0.910 0.003 Black-Eyed Peas 0.000 0.000 0.090 0.004 Brazil Shells 0.000 0.000 1.021 0.003 1.021 0.003 Broccoli 0.000 0.000 0.159 0.008 0.829 0.005 Broccoli 0.000 0.000 1.251 0.004 Broccoli 0.000 0.000 1.077 0.003 Cabbage 0.000 0.000 1.659 0.005 0.858 0.006 Cabbage 0.000 0.000 0.237 0.011 Cabbage 0.677 0.003 0.677 0.003 Carrots 0.000 0.000 1.217 0.004 0.555 0.004 Carrots 0.330 0.002 0.330 0.002 Carrots 0.000 0.000 0.116 0.005 Cauliflower 1.257 0.005 1.257 0.005 1.466 0.005 Cauliflower 0.000 0.000 2.260 0.007 Cauliflower 0.000 0.000 0.882 0.003 Collard Greens 0.986 0.009 0.986 0.009 1.372 0.006 Collard Greens 0.000 0.000 0.571 0.002 Collard Greens 0.000 0.000 2.559 0.007 Corn 0.000 0.000 1.204 0.004 0.506 0.006 Corn 0.000 0.000 0.213 0.010 Corn 0.000 0.000 0.102 0.005 Cucumber 136.830 0.020 136.830 0.020 47.082 0.009 Cucumber 3.339 0.003 3.339 0.003 Cucumber 0.000 0.000 1.078 0.003 Eggplant 0.000 0.000 1.464 0.004 1.425 0.006 Eggplant 0.000 o.ooo 0.126 0.006 Eggplant 0.000 0.000 2.683 0.008 Grapefruit 0.000 0.000 0.095 0.004 0.096 0.005 Grapefruit 0.000 0.000 0.092 0.004 Grapefruit 0.000 0.000 0.101 0.005 97 Actual Reported Averages Pb-210 Ra-226 Pb-210 Ra-226 Pb-210 Ra-226 Item (pCi/g) (PCi/g) (PCi/g) (PCi/g) (PCi/g) (PCi/g) Green Beans 6.489 0.013 6.489 0.013 3.837 0.007 Green Beans 3.987 0.003 3.987 0.003 Green Beans 0.000 0.000 1.035 0.003 Green Onions 0.000 0.000 0.437 0.021 0.852 0.014 Green Onions 0.000 0.000 0.329 0.016 Green Onions 0.000 0.000 1.791 0.005 Green Peppers 0.000 0.000 1.088 0.003 Green Peppers 0.000 0.000 0.102 0.005 Green Peppers 0.000 0.000 0.102 0.005 0.430583 0.004275 Irish Creamer Potatoes 0.000 0.000 0.120 0.006 0.120 0.006 Lemons 0.000 0.000 0.119 0.006 0.414 0.005 Lemons 0.000 0.000 1.008 0.003 Lemons 0.000 0.000 0.114 0.005 Lettuce 0.000 0.000 1.420 0.004 1.237 0.004 Lettuce 0.000 0.000 1.197 0.004 Lettuce 0.000 0.000 1.094 0.003 Lima Beans 1.650 0.000 1.650 0.003 0.963 0.003 Lima Beans 0.324 0.003 0.324 0.003 Lima Beans 0.000 0.000 0.914 0.003 Mustard Greens 1.622 0.017 1.622 0.017 1.622 0.017 Okra 0.000 0.000 1.934 0.006 1.072 0.003 Okra 0.000 0.000 1.000 0.003 Okra 0.281 0.001 0.281 0.001 Onions 0.000 0.000 0.926 0.003 0.599 0.004 Onions 0.000 0.000 0.744 0.002 Onions 0.000 0.000 0.128 0.006 Oranges 0.000 0.000 0.695 0.002 Oranges 1.239 0.002 1.239 0.002 Oranges 0.000 0.000 0.112 0.005 0.682064 0.003214 Parsley 0.000 0.000 0.531 0.025 7.378 0.029 Parsley 0.000 0.000 19.614 0.057 Parsley 0.000 0.000 1.990 0.006 98 Actual Reported Averages Pb-210 Ra-226 Pb-210 Ra-226 Pb-210 Ra-226 Item (pCi/g) (PCi/g) (PCi/g) (PCi/g) (PCi/g) (PCi/g) Peas 0.000 0.000 1.180 0.003 0.821 0.003 Peas 0.259 0.004 0.259 0.004 Peas 0.000 0.000 1.023 0.003 Pole Beans 0.000 0.000 1.307 0.004 0.704476 0.004326 Pole Beans 0.000 0.000 0.102 0.005 Potato 0.000 0.000 0.780 0.002 0.846 0.002 Potato 0.000 0.000 0.863 0.003 Potato 0.000 0.000 0.895 0.003 Purple Hull Peas 0.000 0.000 0.097 0.005 0.453905 0.003469 Purple Hull Peas 0.000 0.000 0.811 0.002 Radishes 0.184 0.004 0.184 0.004 0.580 0.004 Radishes 1.285 0.006 1.285 0.006 Radishes 0.270 0.001 0.270 0.001 Red Potatoes 0.000 0.000 0.109 0.005 0.214874 0.00335 Red Potatoes 0.321 0.002 0.321 0.002 Rice 0.000 0.000 0.073 0.003 Rice 1.290 0.002 1.290 0.002 0.653919 0.002407 Rice 0.000 0.000 0.599 0.002 Spinach 0.000 0.000 0.426 0.020 0.422 0.020 Spinach 0.000 0.000 0.752 0.036 Spinach 0.000 0.000 0.088 0.004 Strawberries 0.000 0.000 1.002 0.003 0.715 0.004 Strawberries 0.000 0.000 0.105 0.005 Strawberries 0.000 0.000 1.038 0.003 Swiss Chard 0.000 0.000 2.010 0.006 2.010 0.006 Tangerine 0.000 0.000 1.265 0.004 0.685906 0.004364 Tangerine 0.000 0.000 0.106 0.005 Tomatoes 0.000 0.000 0.105 0.005 1.011 0.003 Tomatoes 0.000 0.000 0.928 0.003 Tomatoes 1.999 0.002 1.999 0.002 Turnip Greens 1.296 0.009 1.296 0.009 0.941 0.006 Turnip Greens 0.000 0.000 0.135 0.006 Turnip Greens 1.393 0.002 1.393 0.002 99 Actual Reported Averages Pb-210 Ra-226 Pb-210 Ra-226 Pb-210 Ra-226 Item (pCi/g) (PCi/g) (PCi/g) (PCi/g) (PCi/g) (PCi/g) Turnip Root and Green 0.000 0.000 1.841 0.005 1.841 0.005 Turnip Roots 0.491 0.005 0.491 0.005 0.941 0.006 Turnip Roots 0.000 0.000 801.988 2.349 Watermelon 0.000 0.000 0.670 0.002 0.775771 0.002272 Watermelon 0.000 0.000 0.882 0.003 Yellow Corn 0.000 0.000 0.957 0.003 0.680 0.005 Yellow Corn 0.000 0.000 0.181 0.009 Yellow Corn 0.000 0.000 0.903 0.003 Yellow Squash 0.000 0.000 0.937 0.003 0.613 0.004 Yellow Squash 0.784 0.004 0.784 0.004 Yellow Squash 0.000 0.000 0.118 0.006 Zucchini 0.000 0.000 0.096 0.005 0.108 0.005 Zucchini 0.000 0.000 0.114 0.005 Zucchini 0.000 0.000 0.115 0.005 Brazil Nuts 1.324 0.007 1.324 0.007 1.324 0.007 APPENDIX B CRYSTAL BALL OUTPUT DATA 1990 FIPR Data Ra-226 Setl Crystal Ball Output Frequency Chart 20,000 Trials .022 1 — Forecast Total Freqjency Chart .016 .011 .005 .000 221 Outliers 439 44030 KB7 g 59330 rrrern^Br Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 5.92E+00 5.89E+00 6.23E-01 3.88E-01 0.3 3.17 0.11 3.92E+00 8.74E+00 4.81 E+00 4.41 E-03 101 102 1990 FIPR Data Ra-226 Setl Crystal Ball Output Distributions Fitting Chart .033 1 .021 .014 .07 .CCO 40CBO O/erlay Chart Frequency Gbmparison 5OB0 60CBO 7.0C&0 LyuntJ □stritiiian Mhi=591&0 SUQy=622&1 Tea 80C&0 .003 .002 .ODD -0C2 -£CB Overlay Chart Frequency Dfference ■ ■ . . Il I..I. Il.ll I, I. ll.l I llll. I I " ' - "Il I ' ■ «ll ' ii'in p r i — Lyuiibl Dstrilxtiai Mhi=591&0 StiCEy=6235-1 Tcfel 103 1990 FIPR Data Ra-226 Set 2 Crystal Ball Output Frequency Chart 20,000 Trials .021 forecast: Total Frequency Chart 230 Outliers 425 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 5.91 E+00 5.88E+00 6.30E-01 3.97E-01 0.32 3.13 0.11 3.98E+00 9.14E+00 5.16E+00 4.46E-03 104 1990 FIPR Data Ra-226 Set 2 Crystal Ball Output Distributions Fitting Chart 40CBO Overlay Chart Ft eqjency Comparison 50CBO 60CBO 7.QBO Lpgnrrd DstrbJicn NfeBn=5SEB0 SUQy=62&1 TcH 8CIB0 .002 GDI .000 -071 -02 Overlay Chart Frequency Dff erence • ■ ... 1 Id ,i\ 1 1. JLlljiIiI ii» i. ■II PI'I II ■ II i ipi ■h ■■■ ■ UyuirtiDstrhiai Nfean=5£2B0 SUQv=62E1 TcH 40DBO 50C&O 6CCB0 7.0C&O aoceo 105 1990 FIPR Data Ra-226 Set 3 Crystal Ball Output Frequency Chart 20,000 Trials .CE3 1 — .017 .011 .006 .ODD Forecast: Total Frequency Chart 136 Outl ie is 42 431B0 51©0 60IB0 S87BO 339 225 = 113 7.72BO Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 5.92E+00 5.89E+00 6.31 E-01 3.99E-01 0.3 3.15 0.11 3.79E+00 8.89E+00 5.10E+00 4.46E-03 1 990 FIPR Data Ra-226 Set 3 Crystal Ball Output Distributions Fitting Chart 106 4OB0 Overlay Chart Freqjency Comparison 5CDB0 60CBO 7.GCB0 kyuiitJ Dstrtmcn l\fen=5SEB0 Tea aODBO .003 1 -OB Overlay Chart Frequency Dff erence ■ .II . ,ll Jl, .i .iiiil.i. i, ... .. -■■ ■• ■ "II-- in™ "I' i |i-r |i|i - "i 1 1 1 | i ■ "i ■ ■ ■ i ■ • - LujuiidDstrhiicn Nfesn=5SB0 9dQy=62S1 TcB 40CBO 5QBO 60EKD 7.CCB0 aOBO 107 1 990 FIPR Data Ra-226 Set 4 Crystal Ball Output Frequency Chart 20,000 Trials .022 Forecast: Total Frequency Chart tt)Cutiieis -1-432 42EB0 51CB0 591B0 672&0 7SBB0 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 5.92E+00 5.91 E+00 6.29E-01 3.95E-01 0.06 3.04 0.11 3.72E+00 8.63E+00 4.91 E+00 4.45E-03 108 1990 FIPR Data Ra-226 Set 4 Crystal Ball Output Distributions Fitting Chart 40CBO Overlay Chart Frequency Cbmpariscn 5GCBO 7C0BO Mmd CMrtatoi IVbm=5SE&0 &j[*v=6Z&1 TcB accBO .02 T .001 .ODD -C01 -HE j-Mv Overlay Chart Frequency Dfference ■ liilli |IT llll IF ill ill mi Jl_u I I Nond DdriUkn Wfeai=5£E&0 SUCB/=62E-1 TcH 40C&0 50CBO 60C&O 7CC&0 acc&o 109 1990 FIPR Data Ra-226 Set 5 Crystal Ball Output Distributions Fitting Chart 20,000 Trials .022 ■ Forecast: Tota 1 Frequency Chart 201 Outliers 441 591B0 rrrffn^ar 33D7 2205 = 1102 2 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 5.92E+00 5.91 E+00 6.27E-01 3.93E-01 0.05 3.04 0.11 3.50E+00 8.63E+00 5.12E+00 4.44E-03 110 1990 FIPR Data Ra-226 Set 5 Crystal Ball Output Frequency Chart 4CCB0 Overlay Chart Frequency Cbmpariscn 5CCB0 6OB0 7CCB0 BelaDaritita A0b=5OEB-1 B=fcJ=66?&1 Sde=1.3CE+1 TcH aoc&o 0C2 1 " ^ ctjd -D01 -02 Overlay Chart Frequency Dfference • ■ . I.l.l.lll . | L L*J| M .MI 1 1 . ..... '■II III I'l'l 1 1 IP II 1 1 II "II ■ ■■ 1 -1 ' EBaDstribdiai Af*B=50&1 BBa=6S&1 S^e=1.3&-1 TcB 4OB0 50C&O 6CCB0 7.0CBO aa&o Ill 1 990 FIPR Data Ra-226 Set 6 Crystal Ball Output Distributions Fitting Chart 20,000 Trids .022 Forecast: Total Frequency Chart 43&0 512B0 59EBO mrar^ea' 67&0 7.5B0 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 5.92E+00 5.92E+00 6.26E-01 3.91 E-01 0.05 2.97 0.11 3.51 E+00 8.13E+00 4.62E+00 4.42E-03 112 1990 FIPR Data Ra-226 Set 6 Crystal Ball Output Distributions Fitting Chart 4OB0 CX/erlay Chart Frequency GbmparJscn 5CCB0 60CBO 70B0 EBaDslribrticn ArtH=50?&1 EBa=675B-1 Stsle=1.3?&1 TcH acr&o .ODBr .GDI ODD -jooi -JOB '■*■■■ L Overlay Chart Frequency Dfference i.. . I ■ lililll ' r Tffl u -"-»! rn 1 1 i i EBaDstrihlicn A(te=507D-1 Baa=672&1 Sate=13EH TcB 4CCB0 50C&0 6CCBO 70C&O 80CBO 113 1990 FIPR Data Ra-226 Set 6 Crystal Ball Output Distributions Fitting Chart 4QCB0 O/erlay Chart Frequency Comparison 5CCB0 6CCB0 7.CC&0 NjntJ DstrfcLiai l\ten=5SE&0 TcH aa&o .002 r .GDI .ODD -C01 -as. Overlay Chart Frequency Dfference ■ i-i . .Ih ■ _ I PIP UJ y_j ■I l"|l " TTTf Istrrrd QstritUicn Hten=59E*0 SHQv=62£1 TcH 4CCB0 50&0 60C&0 7.0BO aoc&o 114 1 990 FIPR Data Ra-226 Set 7 Crystal Ball Output Frequency Chart 20,000 Trials .023 Forecast: Total Frequency Chart •KJOtJiers 451 4Z&0 SCB&O 59IB0 nieii'yea 67SEH3 E3 7.SE&0 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 5.91 E+00 5.88E+00 6.24E-01 3.89E-01 0.32 3.3 0.11 3.89E+00 1.01E+01 6.23E+00 4.41 E-03 115 1 990 FIPR Data Ra-226 Set 7 Crystal Ball Output Distributions Fitting Chart 4C0BO Overlay Chart Frequency Comparison 5CTBO ifr&fl 7.0CBO LcgnorrrEl Dslrfcubcn Nten=591B0 SfciDEv=6261 Tea aCEBO .QD2 -02 Overlay Chart Frequency Dfference • • ... 1 III. , l\ . j_ ,ll ilII j JjLJii Lij,. ■ "|i r i ■ w i'iii|n|> | ■ 1 LcyuiitJ DslrbJicn r/fean=591&0 3dDB/=63S1 Tea 4OB0 50BO 60B0 7.0C&O 80B0 116 1990 FIPR Data Ra-226 Set 8 Crystal Ball Output Frequency Chart 20,000 Trials .cei Forecast: Total Frequency Chart 229 Cutlers 427 llUdbu, 43S0 51©0 59©0 msrlyeB 673&0 3232 ■ m K 2B5 KB7 7.51B0 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 5.92E+00 5.92E+00 6.24E-01 3.89E-01 0.08 3.04 0.11 3.67E+00 8.95E+00 5.28E+00 4.41 E-03 117 1990 FIPR Data Ra-226 Set 8 Crystal Ball Output Distributions Fitting Chart 4OB0 Overlay Chart Frequency Gbmpariscn 50B0 60B0 7.GCB0 BSaDsbriiilicn Afte=561EH Baa=94EEH SGte=1.S5&1 TcH aoc&o .02 GDI .ODD -GDI -CD2 Overlay Chart Frequency Dfference -VMiW F LijiJil'iliu- ||l I I ■"■! ■ ■ EaaDaribaicri Apte=561B-1 EBa=94E&1 Stzle=1.55EH Tea 40C&O 50C&O 60CBO zccbo acr&o 118 1990 FIPR Data Ra-226 Set 8 Crystal Ball Output Distributions Fitting Chart Overlay Chart Frequency Comparison m r .CED Si S .013 .037 .000 kgnrrel Ddrbiicn Nfean=5S£&0 SdC6/=632E1 Tea 4CCB0 50B0 600BO 7.0B0 acc&o 119 1990 FIPR Data Ra-226 Set 8 Crystal Ball Output Distributions Fitting Chart .(27 1 .(20 : 013 B ■ .1 .007 .QCO 40CBO Overlay Chart frequency Ctmparison 5CCB0 6G0BO 7.GCBO NjndDstribiJin l\fen=5SEB0 3riCB/=S2e-1 TcH aa&o .02 -r .001 tit .ODD -001 -02 Overlay Chart Frequency Dfference ■i l ,i. .ill 1 1 i mr J i ' fm ■l llll ■■■■■" "' Njiibf DstrfaJim Ntei=5S&0 ajD=v=62E1 TcB 1 1 p 1 i 40C&O 5QB0 60CBO 70CBO 80CBO 120 1990 FIPR Data Ra-226 Set 9 Crystal Ball Output Frequency Chart 20,000 Trials .06 1 Forecast: Total Frequency Chart SO Outliers SED ■■•[■*■ — ■— 3CEB-1 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 9.58E+00 5.91 E+00 1.20E+01 1.46E+02 5.08 53.59 1.26 1.59E-01 2.71 E+02 2.70E+02 8.55E-02 121 1990 FIPR Data Ra-226 Set 9 Crystal Ball Output Distributions Fitting Chart QCCBO Q/er lay Chart Freqjency Comparison 1.12&1 225B-1 33E&1 Lcgmral Dslrtiiicn Ktei=99&0 SbDEv=121B-1 Tea 43&1 .QDB .0D1 .ODD -C01 -OB Overlay Chart Frequency Dff erence '.„ ML., . Hi. i.i i ii. ..i .1.1 1 1. ■ 1 |m p. ■ ip 'i'tih ■■ iry'r 1 " ■ v Ixgu 1 1 y DsfrbUicn Nfean=95E+0 SbDB/=121&-1 TcH QCCBO 1.12B-1 22&1 33E&1 4SB-1 122 1990 FIPR Data Pb-210 Setl Crystal Ball Output Frequency Chart 20,000 Trials .022 .017 .011 .006 cm Forecast Total Frequency Chart 2M Outliers 4G 1.5&1 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 2.14E+01 2.13E+01 2.25E+00 5.06E+00 0.32 3.18 0.11 1.45E+01 3.22E+01 1.76E+01 1.59E-02 123 1990 FIPR Data Pb-210 Setl Crystal Ball Output Distributions Fitting Chart CE7 .(23 .013 .CD7 .COO 1.4&1 Overlay Chart Frequency Comparison kgrnrrd DsbibiJcn Mhv=21«H SdDB/=22EKD TcB 1.75B-1 2t&1 2€&1 23&1 .CQ2 -02 Overlay Chart Frequency Dfference ■ ■ , ,l l,l , u li. i . 1 , 1 1 1 , . . ■ ""■■ -lllll - ■ ■ IT i i ii i h | ■'-'"■ i i" ■ L ujund Dslnbicn l\fen=2-^&1 SUC&/=22EK) TcB 1.4&1 1.7SB-1 2t&1 24E&1 28C&-1 124 1990 FIPR Data Pb-210 Set 2 Crystal Ball Output Frequency Chart 20,000 Trids .021 1 — 1 .011 s IS .CDS ODD Forecast Total Frequency Chart tSEM 200 Cutlers 427 2202 2135 1057 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 2.14E+01 2.13E+01 2.25E+00 5.06E+00 0.29 3.1 0.11 1.42E+01 3.24E+01 1.82E+01 1.59E-02 125 1 990 FIPR Data Pb-210 Set 2 Crystal Ball Output Distributions Fitting Chart .035 .019 .013 .OB .000 14B-1 Overlay Chart Frequency Comparison 1.7BB-1 2XEM 24EB-1 LflonoiTSl Dstritutian l\ten=21<&1 SfcJC&/=22©0 Tea 28C&-1 .002 1 .001 .000 -001 -002 Overlay Chart Frequency Dfference - • ..II fall. ■J,„.ll, JW I.I.. ... .11 "IIHIIII '"' 1 III' II 1 ' 1 IficronTEl QstritUicn lvfan=21€H SdC6/=22EB0 Tea 1.4B-1 I7E&1 21C&1 24E&-1 28C&-1 126 1990 FIPR Data Pb-210 Set 3 Crystal Ball Output Frequency Chart 20,000 Trids .GE2 -I — Forecast: Total Frequency Chart Z6 Cutlers 441 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 2.13E+01 2.12E+01 2.26E+00 5.09E+00 0.37 3.27 0.11 1.38E+01 3.35E+01 1.96E+01 1.59E-02 127 1990 FIPR Data Pb-210 Set 3 Crystal Ball Output Distributions Fitting Chart m s m 5 .013 E ■ |g il .07 ■■ ODD 1.4CB-1 Overlay Chart Frequency Comparison 1.75B-1 2t&1 2«f1 LyuiitJ DstnQJjcn Mhi=213&-1 SUC&/=22E&0 TcH 2SB-1 QD2 t .001 .ODD -CD1 -0Q2 CVer lay Chart Frequency Dff erence - . .I..II . .1, 1 1 A jj K*a .il 1 ml i . i ' ' III '1 1 II "1 ,|i,- M I ii ■■. Uxjuii tl DstitUiai Nbn=2t&1 SbC&/=22E*0 Tea 1.4B-1 17E&-1 21C&1 24&1 280E+-1 128 1990 FIPR Data Pb-210 Set 4 Crystal Ball Output Frequency Chart 20,000 Trids .022 R " .011 .CCB .ODD Forecast: Total Frequency Chart 238 Outliers 437 1SB-1 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 2.13E+01 2.13E+01 2.25E+00 5.08E+00 0.06 3.04 0.11 1.21 E+01 3.05E+01 1.84E+01 1.59E-02 129 1990 FIPR Data Pb-210 Set 4 Crystal Ball Output Distributions Fitting Chart m 1 .cm .014 .QDT .ODD 1.4&1 O/erlay Chart Frequency Gbmparisan BaaDsfribiicn Apte=51»-1 Baa=7t&1 Sc~le=50E&-1 TcB 17&1 21C&1 24EM 28C&1 .GCB -OB Overlay Chart Frequency Dfference .... 1 1 .1 lll.lll 1 . 1. U 1 ii l till ■Li i.i. II 1 1 ■ 1 lj 1 r T ||| 1' II Hl|l ■■ ■ • ESaDstritiim Afte=516B-1 B=fca=712&1 Stde=5C6&1 Tea -L4&1 17SEH 2KD-1 24&1 2S&1 130 1990 FIPR Data Pb-210 Set 4 Crystal Ball Output Distributions Fitting Chart CED .014 .007 .ODD 1.4CD-1 O/erlay Chart Frequency Cbmparison Nrtrt DdritUicn Mar=213B-1 &JCEv=22&0 Tea 17&1 21C&-1 24&1 2S&1 GCB -CD3 Overlay Chart Frequency Dfference ... im 1 1. .1 it...!, i I 1 il Jllt- Jk in ... ii- 1 1 1| | "1 i lli " II Fiji'' • Hjrri DstritUicn Mhi=2"EB-1 3dQv=22©0 TcB 1.4B-1 1.7&1 21CB-1 24&1 23&1 131 1990 FIPR Data Pb-210 Set 4 Crystal Ball Output Distributions Fitting Chart .m 1 " .OM .007 CEO 14B-1 O/erlay Chart Frequency Comparison illfc A I III ■ 4 - ^^lllll llfenrrn^ UrpnTTd DstibJiai Mam=2"EB-1 St!Da/=22&0 Tea 175EH 21C&1 24&-1 28C&1 .004 1 .02 .cm -02 -CM Overlay Chart Frequency Off erence ■ . .ml ll. II i.i i 1 ii. ■ in nijiiri'ii 1 i i 1 p ii|'|'| ■•■ ■ • Lxparrt DstribLticn Msn=212B-1 aiQy=2ZEtO Tea 14B-1 17S-1 2t&1 2ffiH 23B-1 132 1990 FIPR Data Pb-210 Set 5 Crystal Ball Output Frequency Chart 20,000 Trids .GE2 1 Forecast Total Frequency Chart 221 Outliers 439 217&1 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 2.14E+01 2.13E+01 2.27E+00 5.15E+00 0.05 3.06 0.11 1.22E+01 3.12E+01 1.90E+01 1.60E-02 133 1990 FIPR Data Pb-210 Set 5 Crystal Ball Output Distributions Fitting Chart O/eriay Chart Frequency Cbmpar tson BetaDslrihiiai AftB=5d&1 Baa=673&1 ade=50B-1 ToB 14EH 17&1 2KB-1 24EB-1 28QB-1 .GC2 -JX2 Overlay Chart Frequency Dfference ■ • ,,h 1 ill ,. 1 1 X. ii ,. ■ "''I'l'lll 1 1 ' ' II ■ II 1 1 1 r ■I if ni ii ■■ - ■ KaQstritUiai Af*B=5Q&1 Baa=672&1 ade=5CC&-1 TcH 1.4B-1 17SEH 2K&1 249&1 28&1 134 1990 FIPR Data Pb-210 Set 5 Crystal Ball Output Distributions Fitting Chart 140EH Orerlay Chart Frequency CbmparisGn 17SEH 2X&-1 24&1 Nrrrel Qstrihlicn l\ten=214&1 3dDEv=22/B0 Tea 28CEH .OB 0D1 Si .ODD -C01 -OB Oeri ay Chart Frequency Dfference • ■ . . l.-lll 1 1 km In. I , ll 1 ., ■l|||l 1 •■)• | r ■ii I| "|l I'l ., |.|| -.,", , | ■ ■ NonmEl DdritUicn Man=21<&1 3dDB/=22?&0 TcH 1.4&1 175&-1 2X&1 24&1 2SB-1 1990 FIPR Data Pb-210 Set 5 Crystal Ball Output Distributions Fitting Chart 135 .CBB .019 JOB .006 .ODD 1.4B-1 Overlay Chart Frequency Cbmpar ison aMl /111 ||l « jTh*. - ... IJ ^I1IIII lllllllllllinTiTTrirrrrrTr^T Uyunil Dstnbicn Mhi=21-&-1 &JDB/=23C&0 Tea 17SB-1 2K&1 24&1 28C&1 .QD3 1 .001 .ODD -C01 -OB Overlay Chart Frequency Dff erence 1 II 1 1 . ll 1 ll 1 1 1 ,.l 1 .ill I.I.I ■'■iii|'|||'i|ii"iV' I. i| I llll"'l • ■^jff Ixy und Dslnbiiicn l\fen=21<&-1 SBC&/=23CBO TcH 1.4B-1 17EEH 2K&1 24&1 28&1 136 1990 FIPR Data Pb-210 Set 6 Crystal Ball Output Frequency Chart 20,000 Trials .CE2 Forecast: Total Frequency Chart B5 Cutlers 433 3292 - 2195 C= KB7 B Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 2.13E+01 2.13E+01 2.28E+00 5.18E+00 0.08 2.99 0.11 1.24E+01 3.14E+01 1.90E+01 1.61E-02 137 1990 FIPR Data Pb-210 Set 6 Crystal Ball Output Distributions Fitting Chart MOEM Overlay Chart Frequency Gbmpariscn 175EH 2KB-1 24&1 Nfcrrrel Dslrititicn l\ten=213B-1 3dC©/=22BB0 TaB 28D-1 Overlay Chart Frequency Qfference .CCB - " .ODD - -flE - mo . , rV „.Jj I ihl.i mi .i pir T[ "in T| 1 '"| ■ Nxn^ Qs&ibiicn Ntean=212B-1 3riCEv=22E&0 TcH MEM 1.7E&1 2KB-1 24&1 260&1 138 1990 FIPR Data Pb-210 Set 7 Ciystal Ball Output Frequency Chart 20,000 Trials .CG3 1 Forecast: Total Frequency Chart -B7 Outliers 451 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 2.14E+01 2.13E+01 2.26E+00 5.09E+00 0.33 3.18 0.11 1.36E+01 3.18E+01 1.82E+01 1.59E-02 139 1990 FIPR Data Pb-210 Set 7 Crystal Ball Output Distributions Fitting Chart .027 .CEO .013 .CCf COD 1.4&1 CVerlay Chart Frequency Qxnpartson 17S-1 2KB-1 24E&1 Lnjumd DstritUian IVten=21<&1 3dCB/=22&0 TcB 28CB-1 .002 .001 .ODD -£01 -£02 CX*rlay Chart Frequency Dfference ■ ■ ... Jl llll . .1 1. i. ii. jl i. ll'| i|'HI Mil 1 1 ■ 1 "l fnir ' ■ ■ L uju ii hl Dstrituticri Mehi=2"1&1 StiGv=22&0 Tea 1.4B-1 17EH 21C&-1 24&1 23CB-1 140 1990 FIPR Data Pb-210 Set 8 Crystal Ball Output Frequency Chart 20,000 Trials .022 forecast: Total Frequency Chart 2)8 Outliers n-447 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 2.14E+01 2.14E+01 2.28E+00 5.18E+00 0.07 3.05 0.11 1.20E+01 3.02E+01 1.81E+01 1.61E-02 141 1990 FIPR Data Pb-210 Set 8 Crystal Ball Output Distributions Fitting Chart 1.4&1 Overlay Chart Frequency Cbmpariscn 17E&I 2K&1 24&1 EaaDaritmcn Afte=531&1 Bfc=812EH Szie=54»-1 TcH 28C&1 .ODB .GDI .ODD -D01 -OB Overlay Chart Frequency Dfference ■ ■ 1 .1 .1 1 1 .. 1 1 1 1 1 II ■J jj,u M i .ii i ii. ■ ■I]! l"""l l"l" l"l"l" l"l ■ [1 '1 PI i| - «|-| -■ r ■■!■ ■ BJaDstritiiicr) AftH=531&-1 ffia=81£H Sde=54&1 Tea "L4&1 175EM 21CB-1 24&1 23B-1 142 1990 FIPR Data Pb-210 Set 9 Crystal Ball Output Frequency Chart 20,000 Trials .06 forecast: Total Frequency Chart 940uUiers — r sob lllfulilllilil; 681 227 1.09&2 -7 14E&2 )> Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 3.47E+01 2.14E+01 4.35E+01 1.89E+03 5.18 56.66 1.25 3.96E-01 9.65E+02 9.65E+02 3.08E-01 90FIPRData Pb-210 Set 9 Crystal Ball Output Distributions Fitting Chart 143 QdBO Overlay Chart Fre qjency Com par i son 37EB-1 7SD-1 1.t&2 Injnmd Dsfrbiicn H/fem=347&1 SbCB/=43S&1 TcH 1.SCB2 .003 f .001 .000 -£D1 -OB 71 Overlay Chart Frequency Off erence llllll, .1 J.ll.,1 !■■ .1 ii »■ » ■■■■■'■■■.,' ■ . ii ||| | I'll" ■■ pmnr'T n v * UjgrrTTEl DslrbJicn NfeBn=347&1 SUCB/=43G&-1 TcB Q0C&O 37E&1 7.SD-1 1.12B2 ISDB2 144 Grocery Store Data Ra-226 Setl Crystal Ball Output Frequency Chart 20,000 Trials .CE2 Fbrecast: Total Frequency Chart 213 Outliers 46 3315 223 1115 341B0 Forecast: Total Statistic Value Trials 20000 Mean 2.70E+00 Median 2.69E+00 Mode — Standard Deviation 2.73E-01 Variance 7.44E-02 Skewness 0.31 Kurtosis 3.22 Coeff. of Variability 0.1 Range Minimum 1.78E+00 Range Maximum 4.06E+00 Range Width 2.27E+00 Mean Std. Error 1.93E-03 145 Grocery Store Data Ra-226 Setl Crystal Ball Output Distributions Fitting Chart .CBB .021 .014 .07 ODD 17EK) Oerlay Chart Frequency Comparison 21SB0 263BO 30B0 LyuntJ DstnbJicn Nten=27C&0 SbD=v=27E-1 TcH 33B0 ODB 1 .GDI .ODD -CD1 -OB Overlay Chart Frequency Dfference ■ . . , ll.llll ,', 1 J ,i il III. I.I .1.. 1... "Ml 1 ■|p '1 ' ■j ■v™ III- | |M" | |i ■ ■ IxyuntJ Dslritiiiai l\ten=27TJBO StJD3/=273&1 TcH 146 Grocery Store Data Ra-226 Set 2 Crystal Ball Output Frequency Chart 20,000 Trials .CB3 1 Forecast: Total Frequency Chart 214 Outliers 462 3C5 ■ 231 = i 1155 g 27CBO rrrarr^ea' 34B0 Forecast: Total Statistic Value Trials 20000 Mean 2.70E+00 Median 2.69E+00 Mode — Standard Deviation 2.75E-01 Variance 7.56E-02 Skewness 0.32 Kurtosis 3.29 Coeff. of Variability 0.1 Range Minimum 1.88E+00 Range Maximum 4.13E+00 Range Width 2.25E+00 Mean Std. Error 1.94E-03 147 Grocery Store Data Ra-226 Set 2 Crystal Ball Output Distributions Fitting Chart CX/erlay Chart Frequency Cbmpari son G&TmaDstribiicn Lx=a6?&i Sde=411&2 9*pe=447&1 ToH 175BO 21EK) 26EBO 30E&O 3SB0 148 Grocery Store Data Ra-226 Set 2 Crystal Ball Output Distributions Fitting Chart CB3 -r .(21 .OM .07 ODD 17»0 CVerlay Chart Frequency Ccmparrscn 219&0 263BO 30SO Nbrrd Dstrbiiai M=m=2XD0 SfclDEy=27S&1 Tea 33B0 .OBI -OB Overlay Chart Frequency Dfference ill 1 ....I..IIIIIIIII.I llll.. ..1 J" 1, Li . 1 If ■ r |,| ■ , -,.|||'..,.||. ■ ■• ~1 • Njtt^ Dstrfaiicn M3an=2XB0 SUC&/=275&1 TcB 175BO 21SB0 26&0 30&0 39B0 149 Grocery Store Data Ra-226 Set 2 Crystal Ball Output Distributions Fitting Chart m : .014 s M « il .007 "™ .arj 17»0 Overlay Chart Frequency Comparison 2-BBO LojuiTd Dsrfaiai l\fen=27E&0 SUCB/=27E&1 Tea 3SD&0 cm 1 001 .coo -coi -CCB Overlay Chart Frequency Dff erence •■ ■ ■ i ■ Yp ' J1U hr JiLu I' I ■! "i rii r "f 17EB0 21G&0 26EBO 30EBO Ixyunbi Darblon Mbi=27C&o SHD3/=27SE1 Tea 3S&0 150 Grocery Store Data Ra-226 Set 3 Crystal Ball Output Frequency Chart 20,000 Trials .CE3 1 .017 .012 QD3 GOD Forecast Total Frequency Chart 164 Cutlers -r4BD 20EBO 241B0 277B0 rrram^ar 31-&0 3505*0 Forecast: Total Statistic Value Trials 20000 Mean 2.70E+00 Median 2.69E+00 Mode — Standard Deviation 2.74E-01 Variance 7.49E-02 Skewness 0.31 Kurtosis 3.15 Coeff. of Variability 0.1 Range Minimum 1.87E+00 Range Maximum 3.93E+00 Range Width 2.06E+00 Mean Std. Error 1.94E-03 151 Grocery Store Data Ra-226 Set 3 Crystal Ball Output Distributions Fitting Chart 17E*0 Overlay Chart Frequency Comparison 21SB0 2SB0 3GEK) G&riTBDslribiiai Loc=Q4BE-1 Sae=42EE2 9^e=414Ef1 Tea 35DBO .CDB JDDI .ceo -mi -OB Overlay Chart Frequency Dfference ■ . . II III, 1 J .,.1 ,.l,l il .. .1. h... ' • ■ '1 II'HI M 1 T |'M||| III' 1" ■ ■ GkTTTBDstribdiai Le=94EE-1 Scde=42E2 Tea 175B0 21SBO 262BO 3G&0 3SBO 152 Grocery Store Data Ra-226 Set 3 Crystal Ball Output Distributions Fitting Chart .(03 .00 .014 .07 .015 1.7EKD Overlay Chart frequency Cbmpariscn 2WB0 262B0 306BO Nfcrrr^ DstrtLBcn l\ten=27CBO SdQv=27S1 Tea 33B0 .OB .GDI .000 -C01 -DOB Overlay Chart Frequency □fference • lllli .„,,.<fljl III 1 , 1 II ,111, Ill ,1. . ■ r 1" ■> ill 1 "!*' ■ '1 '1 NjtteI DjjrtUkn Ma£n=27CBO SUD3/=274&1 Tea 1.7EK) 21SB0 25B0 30BO 3SB0 153 Grocery Store Data Ra-226 Set 3 Crystal Ball Output Distributions Fitting Chart .CEB .021 .014 .ay Overlay Chart Frequency Comparison .coo J — i * 17SB0 2-KBO 26EB0 30EBO Iflgnnti DslrtUicn IYtei=2vT£tO SUC&/=274&1 TcB 33B0 QD2 -02 Overlay Chart Frequency Dfference ■ ' II 1.1 I 1 nil 1 n 1. 1 1. , J. 1 i..i. WW Tr . -||| ™ i • Uyunti DsirbJicn l\fen=27CB0 SfclQy=274&1 TcB ■U5B0 2-EBO 26EB0 3QEB0 3SB0 154 Grocery Store Data Ra-226 Set 4 Crystal Ball Output Frequency Chart 20,000 Trials .CE3 Forecast Total Frequency Chart 175 Outliers 1-451 20BO 23EBO 27030 rrren^H' 3QEO 34B0 Forecast: Total Statistic Value Trials 20000 Mean 2.70E+00 Median 2.70E+00 Mode — Standard Deviation 2.70E-01 Variance 7.28E-02 Skewness 0.02 Kurtosis 2.95 Coeff. of Variability 0.1 Range Minimum 1 .62E+00 Range Maximum 3.71 E+00 Range Width 2.10E+00 Mean Std. Error 1.91E-03 155 Grocery Store Data Ra-226 Set 4 Crystal Ball Output Distributions Fitting Chart .029 .021 .014 .07 .ODD 1.7EK) Overlay Chart Frequency Gbmpariscn 21SB0 26B0 30EO EBaDdrihiicn Apte=52&1 Baa=57S&1 Stde=57tBO TcH 33B0 .QDB-T .001 .an -031 -OB Overlay Chart Frequency Dfference ■ ■ . -i. L. 1 1 1 1 1 r 1 .IhLi L.i. . ■■n 1 1 ■ '1 1 ^ n'li || !■!■ "I ■ ■ EBaDaritilicn Afha=52»1 ffia=57S&1 Sde=57C&0 TcH v&o 219&0 26B0 30B0 33B0 156 Grocery Store Data Ra-226 Set 4 Crystal Ball Output Distributions Fitting Chart .as- .(21 • .ow ■ .007 .GOO 17EK) Overlay Chart Freqjency Comparison 21SBO 26EBO 3QEB0 Loqnorr^ Qslrbiai M3En=270&O StiDE*=2*&1 TcH 3SB0 .004 .002 .000 -02 -CG4 Overlay Chart Frequency Dfference uJ ■■■■-■"""■"lllliTI UlUL krraiTEl Dsbrhiian l\ten=27C&0 SUCEv=274&1 Tea i7S*0 21SB0 262&0 30BBO aso&o 157 Grocery Store Data Ra-226 Set 4 Crystal Ball Output Distributions Fitting Chart 17EB0 Overlay Chart Frequency Comparison HBBO zffibK) 30EBO Njnd DstritLtcn IVfean=27CBO 3dC&/=27TjE1 TcH 33B0 .C0B1 .031 .OD -C01 -OB Overlay Chart Frequency Dfference ■ I....JII ll . I.J.I 1.. 1 . "'II 1 'I 1 •«'i|| 1 J |l |i •! • NcttteI QsbitLticr) M=m=2XEtO StdDs/=27TjE1 Tea 1.7EBO 21£*0 26EBO 3GE&0 3505*0 158 Grocery Store Data Ra-226 Set 5 Crystal Ball Output Frequency Chart 20,000 Trials CE2 1 — Forecast: Total Frequency Chart A3 Outliers 431 3232 2155 1077 15EB0 23B0 26EB0 menses' 3MB0 33B0 Forecast: Total Statistic Value Trials 20000 Mean 2.70E+00 Median 2.70E+00 Mode — Standard Deviation 2.73E-01 Variance 7.47E-02 Skewness Kurtosis 2.95 Coeff. of Variability 0.1 Range Minimum 1.57E+00 Range Maximum 3.77E+00 Range Width 2.21 E+00 Mean Std. Error 1.93E-03 159 Grocery Store Data Ra-226 Set 5 Crystal Ball Output Distributions Fitting Chart 175BO Overlay Chart Frequency Comparison 2-EBO 263BO 3QBB0 ftBDdriliiicn A0b=48E&-1 BBa=49?&1 Stde=5«&0 Toa 3SB0 002 .GDI .ODD -£01 -as. Overlay Chart Frequency Ofference ■ ■ ,, IbLlh.i ,. Lid] 1 II L. LI ■ i .■. ■ "■|«|M, , || I -,| IT r^i II' | "* 1 1 1 I 1" !■■■■'! 1 | ' BBaDariWian AtfB=48E&-1 Baa=49/&-1 Sae=54E&0 ToB 1.7&0 2-EBO 2SB0 30E*O 39CEK3 160 Grocery Store Data Ra-226 Set 5 Crystal Ball Output Distributions Fitting Chart .027 .021 .014 .or .ODD 17EB0 Overlay Chart Frequency Comparison 3GEB0 Nfcrrrd DstribLBcri lfen=27C&0 3dCB/=273&1 TcB 35030 .002 1 -002 Overlay Chart Frequency Dff erence ' lUlli.l i .lull . II. 1. II... ■"■Tll'l |l n 1 "fl r f • Nrrrd Dstntuicn l\ten=27C&0 9dQv=273&1 Tea 17EB0 21EH5 262BO 30E&O 3SB0 161 Grocery Store Data Ra-226 Set 5 Crystal Ball Output Distributions Fitting Chart m (21 .014 m oop .000 V7SBO Overlay Chart Frequency Comparison 21SB0 26B0 30EBO itgoTfi DstribUicn IVban=27C&0 SUQv=27E-1 Tea 35CBO .OOB 1 .002 .000 -0C2 -DOB Overlay Chart Frequency Dfference in. hl.i.liin "iHiimi'i « | ir t ■ ■ ' Lxrarrd DstribUicn Ntei=27C&0 SUDa/=27E&1 Tea IT&O 21EK) 2635K3 30E&O 350&O 162 Grocery Store Data Ra-226 Set 6 Crystal Ball Output Frequency Chart 20,000 Trials .022 1 — Forecast: Total Frequency Chart 179 Cutlers -I-4B 270BO nraTfyaEr Forecast: Total Statistic Value Trials 20000 Mean 2.70E+00 Median 2.70E+00 Mode — Standard Deviation 2.72E-01 Variance 7.40E-02 Skewness 0.04 Kurtosis 3.03 Coeff. of Variability 0.1 Range Minimum 1.68E+00 Range Maximum 3.84E+00 Range Width 2.16E+00 Mean Std. Error 1.92E-03 163 Grocery Store Data Ra-226 Set 6 Crystal Ball Output Distributions Fitting Chart m r .CED • .013 .07 .cm 17EB0 Overlay Chart Frequency Cbmparisai 21EK) 262BO 30EBO B=taQanbtticn Afte=54&1 Baa=68E&1 Stcle=611B0 Tea 33B0 .COBf GDI .GOD -0)1 -OB Overlay Chart Frequency Difference . ■ I III _ ■!■- 1 II mV JL V ■I J A I . . BEtaDsS-ihiicn Afte=54E&1 B=la=68EB-1 Sae=611&0 Tea 175B0 21SB0 262BO 3CSB0 35C&0 164 Grocery Store Data Ra-226 Set 6 Crystal Ball Output Distributions Fitting Chart 17&0 Oreriay Chart Frequency Gbmpariscn 219B0 26B0 303BO Njrrd Qstrtiiai IVfesn=27t&0 SbCb/=27E1 Tea 33B0 .OB .GC2 .ODD -02 -OB Overlay Chart Frequency Qfference ■ hi i J. ... ,i. ,i i,i i. in. ■Jli.i -ill. ' 1 1 ■ _.« ■ mi m r i • p ■ i Nfcnrd Dstrixdoi l\fen=27C&0 StiCEv=275&1 Tea 17»0 21S&0 2SB0 30©o asc&o 165 Grocery Store Data Ra-226 Set 6 Crystal Ball Output Distributions Fitting Chart .CGD .013 .ay .an Overlay Chart Frequency Compar i so n kyoird DstrbJicn Wbm=27C&0 SUDsv=27e&1 TcB 17SB0 21EBO 26B0 3QE&0 3SB0 .QDB .GDI .COD -CD1 Overlay Chart Frequency Dfference • 1 ...Jl mil Lii i. .ij.iii.ii.ni.li ■■■■■n-ii'i||i||||i|' ■ ■ r ic (i ^F i Lxprmd Dstrbion IVfean=27CBO StlC&/=2^1 TcB -OB 17EK) 2-KBO 262BO 30©O 3SB0 166 Grocery Store Data Ra-226 Set 7 Crystal Ball Output Frequency Chart 20,000 Tria"s CG3 1 Forecast: Totd Frequency Chart 235 Oilers — h 45D 271B0 nTsnfyear 34B0 Forecast: Total Statistic Value Trials 20000 Mean 2.70E+00 Median 2.69E+00 Mode — Standard Deviation 2.71 E-01 Variance 7.36E-02 Skewness 0.3 Kurtosis 3.21 Coeff. of Variability 0.1 Range Minimum 1.66E+00 Range Maximum 4.11E+00 Range Width 2.45E+00 Mean Std. Error 1.92E-03 167 Grocery Store Data Ra-226 Set 7 Crystal Ball Output Distributions Fitting Chart .027 1 .CEO .014 .007 .cm 17E*0 Overlay Chart Frequency Comparison 21EK) 262BO 3CEBO G&TmaDslriiiiicn Ur=aC2&1 SEde=38EE2 3*pe=4SE&1 Tea 390&O COB -£CB Overlay Chart Frequency Dffererce ■ ■ ..!.. .1.1 ill ii i i 1 .l.ll l.l.ii.. ... ■■ 'i "" I'l ' Mil ■ r | ''il'l'i il 1 " t ■ ■ GferrrraDstritiiicn lrc=aCE&1 Sc=le=38E&2 ShipB"48BB'1 Tea 17EB0 21&0 26&0 3QE&0 3SBO 168 Grocery Store Data Ra-226 Set 7 Crystal Ball Output Distributions Fitting Chart .(27 1 .CED .014 .C07 .an 1.7EE+0 Overlay Chart Frequency Comparison 2-GE*0 26BO aa&o NjtteI DstrittScn M3m=27CBO 3dQy=271&1 Tdd 3SB0 .ow .02 QCD -CC2 -DM Overlay Chart Frequency Dff erence ■ . ..II.I. Ill.l.ll.l ..II.I illllli i.,lii„, PTPI WT jr i i||ii»-||M ■ 1 1 NkrrrEl Dslribiicri l\ten=270&0 3riCEv=271&1 TcB 175*0 21&0 26B0 aoa&o 2SB0 169 Grocery Store Data Ra-226 Set 7 Crystal Ball Output Distributions Fitting Chart .027 .014 .007 ODD 17EK) Overlay Chart Frequency Comparison 2«BO 263BO 3QEBO LqgroTTBl Ddrtaicn Wfean=27t&0 SUC6/=27I&1 Tea asc&o .OB .GDI QD -GDI -COB Overlay Chart Frequency Dfference • ■ ... 1. .I.J ill ii_I.I_ . i.l i 1 Mi 1 1 ii ..... ■' H IP l|'l |||> 1 1 ■up h' w ■ L uj uii d Oslrhiiai M=m=27C&0 SbQy=271E-1 TcB 17EBO 2-BBO 262&0 3GEB0 33&0 170 Grocery Store Data Ra-226 Set 8 Crystal Ball Output Frequency Chart 20,000 Trids .023 forecast: Total Frequency Chart -B6 Outliers — r- 462 Forecast: Total Statistic Value Trials 20000 Mean 2.70E+00 Median 2.70E+00 Mode — Standard Deviation 2.72E-01 Variance 7.38E-02 Skewness -0.01 Kurtosis 3.02 Coeff. of Variability 0.1 Range Minimum 1.70E+00 Range Maximum 3.79E+00 Range Width 2.09E+00 Mean Std. Error 1.92E-03 171 Grocery Store Data Ra-226 Set 8 Crystal Ball Output Distributions Fitting Chart 17EB0 Cverlay Chart Frequency Comparison 21SB0 2ffiB0 3G6BO BaaDsb-itUion Affta=4SC&-1 EBa=49EH SC=le=541B0 TcB 33B0 .CEB-r .era COD -DD1 -OB Overlay Chart Frequency Dfference ■ ....III ill ...1. .. hi 1 i.i nil ..i ... ■ |ii|i n | i '' 1 i[ - . ■ BaaDSriWcn Af*B=49C&1 Baa=4£E&1 Sde=541B0 TcH 1.7EK) 2-H&0 262BO 30EK) 3SB0 172 Grocery Store Data Ra-226 Set 8 Crystal Ball Output Distributions Fitting Chart .CBB .021 .014 .07 .ODD 1.75BO Overly Chart Frequency Comparison 21EO 263BO 30SO NjrnJ Dstrixtcn l\*an=27TJ&0 SfciQy=272&1 Tea 33B0 .com .0D1 .ODD -fJOl -fXB CVerlay Chart Frequency Dfference • . 1. . .ll .1 1 ill Jillll III. ... 1 1 1 .il. i i... ■■■ >l>llll'lll pi 1 T r 'i in" i M • ttarrsl DstrbJjcn l\ten=27Tj&0 ajQv=27Z-1 Tea 17S0 21SB0 26B0 30&O 3SB0 173 Grocery Store Data Ra-226 Set 8 Crystal Ball Output Distributions Fitting Chart .CBB .021 .014 .07 ODD Overlay Chart Frequency Comparison Lyunti DstritUicn IVter=27rj&0 aiDB/=27E&1 TdEl U8B0 21&0 263&0 30EBO 3S&0 0D3 0Q2 ODD -C02 -CCB Overlay Chart Frequency Dfference =^"1 r jiuikuk Lojund Dstritiijcn IVban=27rj&0 SbC&/=27«-1 Tea 1.7S&0 21&0 2SBO 30SO 35B0 174 Grocery Store Data Ra-226 Set 9 Crystal Ball Output Frequency Chart 20,000 Trials .06 Forecast: Total Frequency Chart 3)9 Outliers 92 lliiHUiiiini fn 73E-2 48S0 95B0 rtTan^ea' 1.4&1 1.91B-1 Forecast: Total Statistic Value Trials 20000 Mean 4.39E+00 Median 2.71 E+00 Mode — Standard Deviation 5.62E+00 Variance 3.16E+01 Skewness 5.6 Kurtosis 69.91 Coeff. of Variability 1.28 Range Minimum 7.33E-02 Range Maximum 1.50E+02 Range Width 1.50E+02 Mean Std. Error 3.98E-02 175 Grocery Store Data Ra-226 Set 9 Crystal Ball Output Distributions Fitting Chart QQC&O Overlay Chart Frequency Comparison 5CIB0 ICDEH 1.3&1 LrgrorrrEl DslrfcUicn l\tei=43EB0 SbCB/=52B0 Tea 20CB-1 .003 1 -CCB T Overlay Chart Frequency Dff erence WWjlW JA **rV»^i Fmi IxyuniJ DstrbJiai M=m=43E&0 SUC&/=55B0 TcB QOCBO 50CBO 10D&1 1.3B-1 2C0&-1 176 Grocery Store Data Pb-210 Setl Crystal Ball Output Frequency Chart 20,000 Trids .023 Forecast: Total Frequency Chart 28 Outliers 4E3 327 2255 1132 677B2 Forecast: Total Statistic Value Trials 20000 Mean 5.18E+02 Median 5.14E+02 Mode Standard Deviation 6.41 E+01 Variance 4.10E+03 Skewness 0.41 Kurtosis 3.26 Coeff. of Variability 0.12 Range Minimum 3.09E+02 Range Maximum 8.72E+02 Range Width 5.63E+02 Mean Std. Error 4.53E-01 177 Grocery Store Data Pb-210 Setl Crystal Ball Output Distributions Fitting Chart 3SB2 Overlay Chart Frequency Comparison 43&2 525B2 612B2 kgrcmnd DslrhJicn SbCe/=63&1 Tea 7.CE&2 .002 1 -02 Overlay Chart Frequency Dff erence ■ . 1 .hill .1 1 J .. .lit,, Ujj .J L.I .. r i ^rr | ||l 1 "|T| ■ liyuiid Dstrbicn Mhi=51£B2 StlCB/=63E&1 TcH 3SB2 43EB2 52E&2 613&2 7.G0&2 178 Grocery Store Data Pb-210 Set 2 Crystal Ball Output Frequency Chart 20,000 Trials .022 forecast: Total Frequency Chart S3 Outliers 48 El I i» 521&2 nTer/yer Forecast: Total Statistic Value Trials 20000 Mean 5.18E+02 Median 5.14E+02 Mode — Standard Deviation 6.46E+01 Variance 4.18E+03 Skewness 0.36 Kurtosis 3.19 Coeff. of Variability 0.12 Range Minimum 3.13E+02 Range Maximum 8.43E+02 Range Width 5.29E+02 Mean Std. Error 4.57E-01 179 Grocery Store Data Pb-210 Set 2 Crystal Ball Output Distributions Fitting Chart 30B-2 Overlay Chart Frequency Comparison 4QC&2 CfcrrraDstritiiicn Le = 1.57B2 SbEle=1.15EH &Bpe=311EH Tea 70B2 ODB 1 -OB CVerlay Chart Frequency Dffererce ■ ■■. ■ '■ M>A h a w IW 1 ^ QnrraDstritiliai loc=1SB2 Sde=1.15EH 9^e=311B-1 Tea 30B2 40C&2 50B2 6QDB2 7CT&2 180 Grocery Store Data Pb-210 Set 2 Crystal Ball Output Distributions Fitting Chart m .CEO .013 .007 .ox 3CCB2 Overlay Chart Frequency Ctmpari son 40CB-2 5CC&2 60DB2 Nxnd Dstrihiicn l\ten=51E&2 SdCB/=64c&-1 Tea 7CC&2 .0C5 -02 Owerlay Chart Frequency Dfference ■ • Lllllllljllll . -Il-ll J, ill Ll-ll . ■W w 1 1 i|| ||i| 1 »| 1 I I Nmrd Dstribicn Nten=51S&2 3dQy=64EH Tea 3CC&2 40CB2 5CC&2 6CCB2 7CC&2 181 Grocery Store Data Pb-210 Set 2 Crystal Ball Output Distributions Fitting Chart m .013 .07 ODD 3CC&2 CVerlay Chart Frequency Comparison 40092 6GC&2 Lxjund Dstritiijai Nten=51£&2 StJD&/=64?&1 TcH 7.CC&2 .003 .001 .ODD -001 -ODB Overlay Chart Frequency Dfference ■ ■ ... ll, .11 III III, .ll 1 iLi 1 "1 III - 1 1 1 ■ " II '"1 •II ipll'l" ■■ LyuiitJ Daribdicn l\fen=51£B2 SUC&/=6<fiB-1 Tea 30C&2 400B2 50032 60C&2 7.CCB2 182 Grocery Store Data Pb-210 Set 3 Crystal Ball Output Frequency Chart 20,000 Trials 022 1 — Fbrecast: Total Frequency Chart £5 Outliers 436 Forecast: Total Statistic Value Trials 20000 Mean 5.18E+02 Median 5.14E+02 Mode — Standard Deviation 6.42E+01 Variance 4.13E+03 Skewness 0.37 Kurtosis 3.23 Coeff. of Variability 0.12 Range Minimum 3.12E+02 Range Maximum 8.53E+02 Range Width 5.41 E+02 Mean Std. Error 4.54E-01 183 Grocery Store Data Pb-210 Set 3 Crystal Ball Output Distributions Fitting Chart 3SB2 Overlay Chart Frequency Comparison 43EB2 52»2 6-CB2 C^rma Dslriliticn im=i.e&2 Sae=1.16&1 3^3e=3CE&1 Tea 70B-2 .02 .001 .ODD -mi -DQ2 Overlay Chart Frequency Dffererce .1, ..l.i.ij mn lil __■! Ij I II . » ■ G&rmaQslrihlJcri L3C=1.9&2 Sae=1.16B-1 3^e=3CEB-1 Tea 3S&2 43&2 52&2 6t&2 7.0&2 184 Grocery Store Data Pb-210 Set 3 Crystal Ball Output Distributions Fitting Chart .CE3 .017 .011 .006 .000 33B-2 O/erlay Chart Frequency Ctmparison jiilAiilrr jfll iiiN JUlHIUIIHUliUlfflllHIiriihh ^JMi M 1 ll 1 lliliw 43E+2 52»2 613B-2 Nfcrrrti QSritUJcn lfei=51£&2 StiQy=642B-1 Tea 7.CT&2 0C4 .002 .000 -032 -0C4 CVerlay Chart Frequency Dffererce III ■ ii.ii.in.ij.. I i. iii lliil L.iliii. . rni iji'i ■ 1 1 iiii i ■■■■-■■ I ■ Nbnrrt Ddritiijari Nten=51fi&2 SfcJCEv=64&1 Tea 33&2 43EB2 52&2 613B-2 70&2 185 Grocery Store Data Pb-210 Set 3 Crystal Ball Output Distributions Fitting Chart 35C&2 Overlay Chart Frequency Comparison 43EB2 52E2 6t&2 l£gmm=l nslrtiiian Mhi=518B2 SUDb/=643B-1 TcH 7.CC&2 .02 .GDI .000 -J0O1 -02 Overlay Chart Frequency Off erence AA aA rn I ill. ..Hi h I I.I ll.i H r Mi I 1 W LcgnorrrEl DslrfcUicn Htei=518&2 SUCB/=64B-1 TcB 3S&2 43EB2 52E&2 6t&2 7.0C&2 186 Grocery Store Data Pb-210 Set 4 Crystal Ball Output Frequency Chart 20,000 Trials .023 .017' .011 .003 ODD ih.iiilll Forecast: Total Frequency Chart ■60 Cutlers 453 3S&2 Forecast: Total Statistic Value Trials 20000 Mean 5.18E+02 Median 5.16E+02 Mode Standard Deviation 6.47E+01 Variance 4.18E+03 Skewness 0.2 Kurtosis 3.08 Coeff. of Variability 0.12 Range Minimum 2.82E+02 Range Maximum 8.70E+02 Range Width 5.88E+02 Mean Std. Error 4.57E-01 187 Grocery Store Data Pb-210 Set 4 Crystal Ball Output Distributions Fitting Chart .CBD .013 .007 .ODD 30CE+2 Overt*/ Chart Frequency Cbmparison jjj| iJjjKi ■ jdjl ||[|K i- >jjjj IllhnTTTTi 4CC&2 50E+-2 6QC&2 GErrrraDslrihicn Le,=-12&2 Stde=647BO 3TEpe=9SEEH TcB 7.Q&2 .02 .GDI .ODD -031 -02 Overlay Chart Frequency Dfference ■ 1. .Ill Jill 1 ni lh 1 1 III i . . i..l L .. - ■ M f f || II' I ■ 'III ■ i r 'i n| >i|i ■ ! ■ G&nTaDstriiiiJcn lffi=-12SB2 Stcle=647B0 3^b=99E&1 Tea 30B2 40032 50CB2 6CEB2 7.0032 Grocery Store Data Pb-210 Set 4 Crystal Ball Output Distributions Fitting Chart .(27 1 .CBD .013 .007 .ODD 3CC&-2 Overlay Chart Frequency Cbmpari son 4CC&2 5CD&2 60C&2 Ntrrrd Dsbritiiicn Mhi=51E&2 SfciD3/=64/B-1 Tea 7.0CEf2 XDB1 -03 O/erlay Chart Frequency DfFererce . I 1 i.i.i. illlil- 1 L in hi 1 ll.lil.. il.ii 'l'| ill 1 | '|H 1 1 1 —i • Nmnd DstritUicn IVfem=51SB-2 SHD=v=64&1 TaB 30B-2 4CT&2 50CB2 6CTB2 7.GCB2 189 Grocery Store Data Pb-210 Set 4 Crystal Ball Output Distributions Fitting Chart .027- .cm .013 .007 COO 30B2 O/erlay Chart Frequency Comparison 4CT&2 50C&2 60B2 LyuiittDslrtUJcn Mar=51E&2 StlCfv=65&1 Tea 7.CC&2 .003 f .002 .ODD -CC2 -OB Overlay Chart Frequency Dfference ,. ■ hi j. - •-■■i|i— i |jr| llJlillu. i lUl. ||'|| I'j ■ T pr Lqjrrmd DslrhJicri l\tei=51EB2 SbCB/=65&1 TcH 3CCB2 40C&2 5C0&2 60CE+2 7.QC&-2 190 Grocery Store Data Pb-210 Set 5 Crystal Ball Output Frequency Chart 20,000 Trials .022 .016 .011 .CD5 .ODD •uiimii Forecast: Total Frequency Chart 237CU)iers 433 357B2 Forecast: Total Statistic Value Trials 20000 Mean 5.18E+02 Median 5.16E+02 Mode — Standard Deviation 6.39E+01 Variance 4.09E+03 Skewness 0.21 Kurtosis 3.12 Coeff. of Variability 0.12 Range Minimum 3.02E+02 Range Maximum 8.43E+02 Range Width 5.41 E+02 Mean Std. Error 4.52E-01 191 Grocery Store Data Pb-210 Set 5 Crystal Ball Output Distributions Fitting Chart 33B2 Overlay Chart Frequency Cbmparison GfrmBDslritiiian Lcc=-1.1£t2 Sae=64B0 Tea 43&2 52&2 613B-2 7GDB2 .02 .001 .ODD -£D1 -02 Overlay Chart Frequency Dffererce • ■ ..J Jl Jill , ,ll .1,1. J ,1.1 .i. "in ip | || ||'n| r |ri| ■ n ii IP i- i"-"i|'-i QnTTBDslriliticn lffl=-fHB2 Stde=64B0 3^e=99fB-1 Tea 3S&2 43&2 52»2 612B2 7.0&2 192 Grocery Store Data Pb-210 Set 5 Crystal Ball Output Distributions Fitting Chart Overlay Chart Frequency Comparison 3SB-2 43»2 52&2 6t&2 Nfcrrrt Daribdicn ltei=5ia&2 8dDB/=63EEH Tea 7QDB-2 .003 0D1 CCD -JDD1 -OB Overlay Chart Frequency Dfference • ■ JJ.il .III i .1 J ,in JU Jill J . ■ |. -. 1" II 1 IP ll.llll-ll- 1 1 ■ Nrmd Dsb-ibiiGn Mhi=51S&2 Tea 193 Grocery Store Data Pb-210 Set 5 Crystal Ball Output Distributions Fitting Chart 33B-2 O/erlay Chart Frequency Comparison 6T&2 LyuntJ Dstrbiicn l\feri=51E&-2 SUDev=646EH Td3l 7.0CB2 .003 1 -OB Overlay Chart Frequency Off erence ■ • .II ,lll iJuL ...,i. . I uLi.i.1... l'lllll'IIH jl ■ ■ 1 PI 11 ! 1 Hi" i- ■ ■ Injund Dsfrhiian l\*m=518E+2 StlCB/=&€B-1 TcB 33B2 43E&2 525B2 613B2 7.0C&2 194 Grocery Store Data Pb-210 Set 6 Crystal Ball Output Frequency Chart 20,000 Trials .022 Forecast: Total Frequency Chart 210 Outliers T 434 3255 217 KB5 67&2 Forecast: Total Statistic Value Trials 20000 Mean 5.17E+02 Median 5.14E+02 Mode — Standard Deviation 6.38E+01 Variance 4.07E+03 Skewness 0.22 Kurtosis 3.14 Coeff. of Variability 0.12 Range Minimum 2.69E+02 Range Maximum 8.45E+02 Range Width 5.76E+02 Mean Std. Error 4.51 E-01 195 Grocery Store Data Pb-210 Set 6 Crystal Ball Output Distributions Fitting Chart 3S&2 Overlay Chart Frequency Comparison 43&2 52&2 6t&2 C^rmaDstritUlcn Lr.=-79B-1 Sae=68EB0 9^e=a6E&1 Tea 7CCB2 .GD3 1 O/erlay Chart Frequency Dffererce -OB ■ ..i Lull ill J III. ,il 1 1 hi i .......I. . . I' "M | | " • i ■ 1 1' jipni I.- ■ • ■ GbTrraDstritilicn lo:=-7.aB-1 Sde=686BO 9q£=86EH Tea 33B2 43&2 52SB2 613B2 7.0B2 196 Grocery Store Data Pb-210 Set 6 Crystal Ball Output Distributions Fitting Chart 3SB2 Overlay Chart Frequency Comparison 43&2 52&2 6-G&2 Nbml DdriWicn Nfem=517&2 adDB/=63E&1 Tcfei 7.GC&2 QDB .GDI .ODD -001 -OB Overlay Chart Frequency Dfference ■ ■ ..hi ill 1 1 , 1 . I 1 1 1. ill. i i i '■ m "ff nrif |i> r i I'pii |i«"'i ■ t^trrrd QstritxEan l\*ai=517&2 atCB/=63&1 TcfcJ 39B2 43EB2 52&2 613&2 7.0C&2 197 Grocery Store Data Pb-210 Set 6 Crystal Ball Output Distributions Fitting Chart 3SB-2 Overlay Chart Frequency Campari son 43EB-2 6t&2 Lxpjrrcl Dslrbicn Htei=517&2 TcB 7.0&2 .OB .001 .ODD -DD1 -az Overlay Chart Frequency Qfference III J 1 .IL ..1 ■ i 1 illlll.iil. ■■ ■■" "Jll " "1 1'l »" M ' 1 'I II ll'l'l'" ' • ky untJ DdrhJicn Nten=517B2 adDa/=64&1 TcB 3SB2 43EB2 52&2 612&2 7.CC&2 198 Grocery Store Data Pb-210 Set 7 Crystal Ball Output Frequency Chart 20,000 Trials .CE3 .017 .011 .006 .ODD Forecast: Total Frequency Chart 221 Outliers HS9 35EB-2 43B&2 521&2 rrr&rtyB 6CE&2 68EB2 Forecast: Total Statistic Value Trials 20000 Mean 5.18E+02 Median 5.14E+02 Mode — Standard Deviation 6.47E+01 Variance 4.18E+03 Skewness 0.39 Kurtosis 3.26 Coeff. of Variability 0.12 Range Minimum 3.04E+02 Range Maximum 8.33E+02 Range Width 5.29E+02 Mean Std. Error 4.57E-01 199 Grocery Store Data Pb-210 Set 7 Crystal Ball Output Distributions Fitting Chart .(EM .GED £ -■ m = .013 E — i SI .007 "™ .000 3CCB2 Overlay Chart Frequency Comparison 40CB-2 50CB2 60CB2 Lcgrcrrrd Dslrbicn Nban=51EB2 SUCB/=64B&1 TcH 7.0C&2 .002 T .001 .000 -fJDl Overlay Chart Frequency Dff ererce .. .1.11,1, „i..„i,i„ I'M ||l||| JllJ PT[ I ilj J... i j ■- » in ■■■ i pir LcgxnTEl DstrbJcn lvfen=518&2 StlCEv=646&1 Tea -J002 I r 3CC&2 400&2 500B-2 600B2 7.0C&2 200 Grocery Store Data Pb-210 Set 8 Crystal Ball Output Frequency Chart 20,000 Trials .023 1 — Forecast: Total Frequency Chart Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 5.18E+02 5.16E+02 6.37E+01 4.06E+03 0.21 3.16 0.12 2.75E+02 8.04E+02 5.29E+02 4.50E-01 201 Grocery Store Data Pb-210 Set 8 Crystal Ball Output Distributions Fitting Chart 39CB2 Overlay Chart Frequency Cbmpari son 43EB2 529=f2 613B-2 GfrmaDslribiJcn loc=-1.1£B2 Sde=637&0 S^£=9SC©-1 Toa 7.CE&2 .002 1 .cm .OD -mi -J0C2 Overlay Chart Frequency Dffererce ■ •ilLiI.ii lL. , ^J. IjJ .1.1 1 i - i" -| |" i| '|'||ii | | | 'III' l|l|-ill"« ■ GSTmaQstritiiicn Lr=-1.1&2 Stde=637BO TcB 33B2 43&2 52»2 6t&2 7CC&2 202 Grocery Store Data Pb-210 Set 8 Crystal Ball Output Distributions Fitting Chart 3SB2 CVerlay Chart Frequency Comparison 43E&2 52EB2 613&2 Nrmd DstribUicn l\*ai=518B2 adCB/=63&1 Tea 7GCB-2 .003 -OB Overlay Chart Frequency Dfference TPfT M Tn"nr mnr htnrt Dstritita Msn=5ie&2 3dQy=637B-1 ToB 3S&2 43&2 52Et2 613&2 70C&2 203 Grocery Store Data Pb-210 Set 8 Crystal Ball Output Distributions Fitting Chart 3SB2 Overlay Chart Frequency Comparison 43E&2 52»2 6t&2 IxguniJ DstrbJicn Wfem=518fr2 SbD=v=64&1 Tea 7.GC&-2 .003 .GDI .000 -OCT -DOB Overlay Chart Frequency Dfference II ■ ..,,1,1 ill III. J. Li i l.i 1 1 . H..... p '\yy i i I'l 1 IPfl ■ T V H) . Ixyund D^rtUiai IVten=5ia&-2 SBCEy=64&1 Tea 35CB2 43E&2 52E*2 6t&2 7.0C&2 204 Grocery Store Data Pb-210 Set 9 Crystal Ball Output Frequency Chart 20,000 Trials .06 Forecast: Total Frequency Chart SD2 Outliers ST ''■[■■■ 26EB3 68D2 4535 E 2237 35E&3 Forecast: Total Statistic Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 20000 8.44E+02 5.25E+02 1.08E+03 1.16E+06 6.02 86.32 1.27 1.00E+01 3.15E+04 3.15E+04 7.61 E+00 205 Grocery Store Data Pb-210 Set 9 Crystal Ball Output Distributions Fitting Chart QQGBO Overlay Chart Frequency Comparison 1.0CB3 20E+-3 3CCB3 L aroirri DsWhlcn Nfean=84&2 SHC&/=1.07&3 TcB 40CB3 .ODB .GDI oro -JDD1 -OB Overlay Chart Frequency Dfference • K ^ J 1 iJlil.li.1 .1. i .. ii.. i i Till | r ' r kgurrd DsbibUian Msi=84&2 StJC&/=1.0?&-3 Tea Q0CBO ■LCCB3 2CTJB3 3CD&-3 40&3 REFERENCES Argonne National Laboratories (ANL) (1989). Residual Radiation Dose Contamination Program-RESRAD . http://web.ead.anl.gov/resrad. Birky, B. (1990). Dose Assessment From Radioactivity in Foods Grown on Mined Florida Phosphate Lands . Master's thesis, University of Florida, Gainesville, FL. Borrud, L., Enns, C. W., & Mickle, S. 1996. What We Eat in America: USDA Surveys Food Consumption Changes. Food Review 14-15 Burk, R. J., Jr. (2000). Risk Assessment: Position Statement of the Health Physics Society . McLean, VA: Health Physics Society. Carvalho, F. P. (1995). 210 Polonium and 210 Lead Intake by the Portuguese Population: The Contribution of Seafood in the Dietary Intake of 210 Polonium and 210 Lead. Health Physics 69(4): 469-480. Decisioneering. (1996). Crystal Ball 4.0 User Manual . Denver, CO: Author. Enns, C. W., Goldman, J. D., & Cook, A. (1997). Trends in food and nutrient intakes by adults: NFCS 1977-78, CSFII 19889-91, and CSFII 1994-95. Family Economics and Nutrition Review 10(4): 1-15. Environmental Protection Agency. (1988). Limiting Values of Radionuclide Intake and Air Concentration and Dose Conversion Factors for Inhalation. Submersion, and Ingestion . Oak Ridge, TN, Oak Ridge National Laboratory. Environmental Protection Agency. (1995). Cancer Risk Coefficients for Environmental Exposure to Radionuclides: Federal Guidance Report No. 13 . (Document 402-R9- 9001). Washington, DC: Author. Environmental Protection Agency. (1997). Exposure Factors Handbook. Vol. H-Food Ingestion Factors (Document 600/P-95/002Fa). Washington, DC: Author. Guidry, J. J., Bolch, W. E., Roessler, C. E., McClave, J. T., & Moon, J. R. (1986). Radioactivity in Foods Grown on Florida Phosphate Lands . Bartow, FL, Florida Institute of Phosphate Research. 206 207 Guidry, J. J., Roessler, C. E., Bolch, W. E., McClave, J. T., Hewitt, C. C, & Abel, T. E. (1990). Radioactivity in Foods Grown on Mined Phosphate Lands . Bartow, FL, Florida Institute of Phosphate Research. Harley, J. W. (1988). Naturally occurring sources of radioactive contamination. In J. H. Harley, G. D. Schmidt, and G. Silini (Eds.), Radionuclides in the Food Chain (pp. 58-71). New York: Springer-Verlag. International Council on Radiation Protection (1994). Dose Coefficients for Intakes of Radionuclides by Workers. Annals of the ICRP 24(4): 1-83. International Council on Radiation Protection (1996). Age-dependent Doses to Members of the Public from Intake of Radionuclides: Part 5 Compilation of Ingestion and Inhalation Dose Coefficients. Annals of the ICRP 26(1): 1-89. Linsalata, P. (1994). Uranium and Thorium Decay Series Radionuclides in Himan and Animal Foodchaines~A Review. Journal of Environmental Quality 23: 633-642. Morse, R. S. & Welford, G. A. (1971). Dietary Intake of 210Pb. Health Physics 21: 53- 55. Nuclear Regulatory Commission (1977). Regulatory Guide 1.109: Calculation of Annual Doses to Man from Routine Releases of Reactor Effluents for the Purpose of Evaluating Compliance with 10 CFR Part 50, Appendix I. Regulatory Guide 1.109 . Washington, DC: Author. Nuclear Regulatory Commission (2000). NRC Mission . May 11, 2000. www.NRC.gov. Pennington, J. A. T. (1983). Revision of the Total Diet Study, Food List and Diets. Journal of the American Dietetic Association 82f2): 166-173. Pennington, J. A. T. (1992). Total Diet Studies: The 1990 Revision of the FDA Total Diet Study. Journal of Nutritional Education 24(4): 173-178. Pritchard, P. C. H., & Bloodwell, J. M. (1985). Multidisciplinarv Study of Radionuclides and Heavy Metal Concentrations in Wildlife on Phosphate Mined and Reclaimed Lands . Maitland, FL, Audubon Society. Shleien, B., Slaback, L. A., Jr., & Birky, B. K. (1998). Handbook of Health Phvsics and Radiological Health . Baltimore, MD: Williams and Wilkins. Turner, J. E., Bogard, J. S., Hunt, J. B., & Rhea, T. A. (1988). Problems and Solutions in Radiation Protection. Elmsford, NY: Pergamon Press. 208 U.S. Department of Agriculture (USDA). (1996). Continuing Food Survey of Intake by Individuals II. (http://www.barc.usda.gov/bhnrc/foodsurvey/cfsii94.html). U.S. Department of Commerce. (1983). Radiological Assessment: A Textbook on Environmental Dose Analysis : Oak Ridge, TN, NTIS. Weiner, E. R. (2000). Applications of Environmental Chemistry . Boca Raton, FL: Lewis Publishers. Yu, K. N., & Mao, S. Y. (1999). Assessment of Radionuclide Contents in Food in Hong Kong. Health Physics 77(6): 686-696. BIOGRAPHICAL SKETCH Ward L. Dougherty was bom in Stamford, Connecticut, on February 27, 1963. He was raised in Lutz, Florida. He joined the Navy in December 1986. He met and married his wife, Gwendolyn Bennett, while in the Navy on August 18, 1990. His son, Justin, was bom while he was stationed in Charleston, South Carolina, on August 24, 1991. His daughter, Michelle, was bom just prior to completing his Naval service on February 5, 1993. He served on board two submarines, the U.S.S. James Madison (SSBN 627) and the U.S.S. Dolphin (AGSS 555). He achieved the engineering watch supervisor and engineering duty petty office qualification while on board the Madison. As an E-5 he was one of only two people to ever qualify, in the 30-year history of the boat, to that watchstation at his rank. His awards include Humanitarian, Good Conduct (2), Sea Service Ribbon, National Defense Service Medal, and the Submarine Qualification with four patrol pins. He completed over six years with ah honorable discharge in March 1993. He attended the University of Florida, College of Engineering, Department of Nuclear and Radiological Engineering, from April 1993 until May 1999. He worked for Innovative Nuclear Space Power and Propulsion Institute from 1996-1999 and has attended numerous space nuclear power conferences. He graduated from nuclear engineering with a bachelor's degree with high honors in August 1996 and with a master's degree in December 1999. He transferred to environmental engineering and subsequently 209 210 dual enrolled in nuclear and environmental to pursue concurrent Ph.D. degrees in nuclear engineering and environmental engineering. I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. W. Emmett Bolch, Jr., Chair Professor of Environmental Engineering Sciences I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Wesley E. Bol£h Wesley Associate Professor of Nuclear and Radiological Engineering I certify' that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. fate- William S. Properzio i. Associate Professor of Environmental Engineering Sciences I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. U n : f G. Ronald Dalton Professor of Nuclear and Radiological Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Jtt<~ -*?• >^w Angela/S. Lindner Assistant Professor of Environmental Engineering Sciences This dissertation was submitted to the Graduate Faculty of the College of Engineering and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy May 2001 / M. 73ck Ohanian Dean, College of Engineering Winfred M. Phillips Dean, Graduate School Lb 7bo\ UNIVERSITY OF FLORIDA 3 1262 08555 1751